Projekt

2025-01-29

Wstęp

Opis problemu

Problemem, który analizujemy w niniejszym projekcie jest wpływ poszczególnych czynników na wynik końcowy ucznia (?)

Baza danych

Baza danych którą analizujemy nazywa się „Wyniki uczniów”. Znajduje się w niej 20 kolumn z danymi oraz 6.608 wierszy danych. W bazie danych znajdują się zarówno zmienne liczbowe jak i jakościowe.

## Rows: 6,607
## Columns: 20
## $ Hours_Studied              <int> 23, 19, 24, 29, 19, 19, 29, 25, 17, 23, 17,…
## $ Attendance                 <int> 84, 64, 98, 89, 92, 88, 84, 78, 94, 98, 80,…
## $ Parental_Involvement       <chr> "Low", "Low", "Medium", "Low", "Medium", "M…
## $ Access_to_Resources        <chr> "High", "Medium", "Medium", "Medium", "Medi…
## $ Extracurricular_Activities <chr> "No", "No", "Yes", "Yes", "Yes", "Yes", "Ye…
## $ Sleep_Hours                <int> 7, 8, 7, 8, 6, 8, NA, 6, 6, 8, 8, 6, 8, 8, …
## $ Previous_Scores            <int> 73, 59, 91, 98, 65, 89, 68, 50, 80, 71, 88,…
## $ Motivation_Level           <chr> "Low", "Low", "Medium", "Medium", "Medium",…
## $ Internet_Access            <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "…
## $ Tutoring_Sessions          <int> 0, 2, 2, 1, 3, 3, 1, 1, 0, 0, 4, 2, 2, 2, 1…
## $ Family_Income              <chr> "Low", "Medium", "Medium", "Medium", "Mediu…
## $ Teacher_Quality            <chr> "Medium", "Medium", "Medium", "Medium", "Hi…
## $ School_Type                <chr> "Public", "Public", "Public", "Public", "Pu…
## $ Peer_Influence             <chr> "Positive", "Negative", "Neutral", "Negativ…
## $ Physical_Activity          <int> 3, 4, 4, 4, 4, 3, 2, 2, 1, 5, 4, 2, 4, 3, 4…
## $ Learning_Disabilities      <chr> "No", "No", "No", "No", "No", "No", "No", "…
## $ Parental_Education_Level   <chr> "High School", "College", "Postgraduate", "…
## $ Distance_from_Home         <chr> "Near", "Moderate", "Near", "Moderate", "Ne…
## $ Gender                     <chr> "Male", "Female", "Male", "Male", "Female",…
## $ Exam_Score                 <int> 67, 61, 74, 71, NA, 71, 67, 66, 69, 72, 68,…

Czyszczenie danych

W niniejszym rozdziale sprawdzimy jakość danych, zbadamy występowanie braków danych oraz dobierzemy odpowiednią metodę imputacji brakujących danych (jeżeli zajdzie taka potrzeba).

Walidacja danych

Zostało wykonane badanie danych za pomocą funkcji aggr. Wykres po lewej stronie prezentuje proporcje braków danych. W naszym przypadku największe braki występują w trzech zmiennych:

  • Sleep Hours - 5,22%
  • Exam Score - 4,37%
  • Distance from Home - 1,01%

Tabela po prawej stronie ilistruje współwystępowanie braków w zestawie danych. Czerwone pola oznaczają brakujące wartości. Można zauważyć, że brakujące dane są dość rozporoszone i nie występują jednocześnie w wielu zmiennych. Oznacza to, że nie instnieje współzależność pomiędzy występowaniem braków więc dane brakujące będziemy uzupełniać za pomocą podobieństwa.

aggr(czynniki, numbers = TRUE, sortVars = TRUE)

## 
##  Variables sorted by number of missings: 
##                    Variable      Count
##                 Sleep_Hours 0.05297412
##               Family_Income 0.05297412
##                  Exam_Score 0.04540639
##    Parental_Education_Level 0.01362192
##             Teacher_Quality 0.01180566
##          Distance_from_Home 0.01014076
##               Hours_Studied 0.00000000
##                  Attendance 0.00000000
##        Parental_Involvement 0.00000000
##         Access_to_Resources 0.00000000
##  Extracurricular_Activities 0.00000000
##             Previous_Scores 0.00000000
##            Motivation_Level 0.00000000
##             Internet_Access 0.00000000
##           Tutoring_Sessions 0.00000000
##                 School_Type 0.00000000
##              Peer_Influence 0.00000000
##           Physical_Activity 0.00000000
##       Learning_Disabilities 0.00000000
##                      Gender 0.00000000
gg_miss_upset(czynniki)

Wykres poniżej został stworzony za pomocą funkcji gg_miss_upset. Prezentuje on wartości liczbowe brakujących danych

  • Family income – 309
  • Sleep Hours – 300

Z uwagi na stosunkowo wysoką ilość braków dokonamy imputacji danych.

czynniki1<- czynniki[!is.na(czynniki$Family_Income), ]
czynniki2<- czynniki1[!is.na(czynniki1$Parental_Education_Level), ]
czynniki3<- czynniki2[!is.na(czynniki2$Teacher_Quality), ]
czynniki4<- czynniki3[!is.na(czynniki3$Distance_from_Home), ]
unique(czynniki4$Family_Income)
## [1] "Low"    "Medium" "High"
unique(czynniki4$Parental_Education_Level)
## [1] "High School"  "College"      "Postgraduate"
unique(czynniki4$Teacher_Quality)
## [1] "Medium" "High"   "Low"
unique(czynniki4$Distance_from_Home)
## [1] "Near"     "Moderate" "Far"
glimpse(czynniki4)
## Rows: 6,038
## Columns: 20
## $ Hours_Studied              <int> 23, 19, 24, 29, 19, 19, 29, 25, 17, 17, 17,…
## $ Attendance                 <int> 84, 64, 98, 89, 92, 88, 84, 78, 94, 80, 97,…
## $ Parental_Involvement       <chr> "Low", "Low", "Medium", "Low", "Medium", "M…
## $ Access_to_Resources        <chr> "High", "Medium", "Medium", "Medium", "Medi…
## $ Extracurricular_Activities <chr> "No", "No", "Yes", "Yes", "Yes", "Yes", "Ye…
## $ Sleep_Hours                <int> 7, 8, 7, 8, 6, 8, NA, 6, 6, 8, 6, 8, 8, NA,…
## $ Previous_Scores            <int> 73, 59, 91, 98, 65, 89, 68, 50, 80, 88, 87,…
## $ Motivation_Level           <chr> "Low", "Low", "Medium", "Medium", "Medium",…
## $ Internet_Access            <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "…
## $ Tutoring_Sessions          <int> 0, 2, 2, 1, 3, 3, 1, 1, 0, 4, 2, 2, 2, 1, 2…
## $ Family_Income              <chr> "Low", "Medium", "Medium", "Medium", "Mediu…
## $ Teacher_Quality            <chr> "Medium", "Medium", "Medium", "Medium", "Hi…
## $ School_Type                <chr> "Public", "Public", "Public", "Public", "Pu…
## $ Peer_Influence             <chr> "Positive", "Negative", "Neutral", "Negativ…
## $ Physical_Activity          <int> 3, 4, 4, 4, 4, 3, 2, 2, 1, 4, 2, 4, 3, 4, 4…
## $ Learning_Disabilities      <chr> "No", "No", "No", "No", "No", "No", "No", "…
## $ Parental_Education_Level   <chr> "High School", "College", "Postgraduate", "…
## $ Distance_from_Home         <chr> "Near", "Moderate", "Near", "Moderate", "Ne…
## $ Gender                     <chr> "Male", "Female", "Male", "Male", "Female",…
## $ Exam_Score                 <int> 67, 61, 74, 71, NA, 71, 67, 66, 69, 68, 71,…
gg_miss_upset(czynniki4)

aggr(czynniki4, numbers = TRUE, sortVars = TRUE)

## 
##  Variables sorted by number of missings: 
##                    Variable      Count
##                 Sleep_Hours 0.05266645
##                  Exam_Score 0.04372309
##               Hours_Studied 0.00000000
##                  Attendance 0.00000000
##        Parental_Involvement 0.00000000
##         Access_to_Resources 0.00000000
##  Extracurricular_Activities 0.00000000
##             Previous_Scores 0.00000000
##            Motivation_Level 0.00000000
##             Internet_Access 0.00000000
##           Tutoring_Sessions 0.00000000
##               Family_Income 0.00000000
##             Teacher_Quality 0.00000000
##                 School_Type 0.00000000
##              Peer_Influence 0.00000000
##           Physical_Activity 0.00000000
##       Learning_Disabilities 0.00000000
##    Parental_Education_Level 0.00000000
##          Distance_from_Home 0.00000000
##                      Gender 0.00000000

Imputacja danych

as.numeric(czynniki4$Exam_Score)
##    [1]  67  61  74  71  NA  71  67  66  69  68  71  70  66  65  64  60  65  67
##   [19]  66  69  72  66  66  63  65  71  66  64  69  67  68  61  64  67  63  NA
##   [37]  67  65  64  70  68  65  68  64  68  63  64  67  67  66  72  65  71  66
##   [55]  68  70  62  68  71  68  69  NA  69  65  70  71  65  72  69  66  68  65
##   [73]  60  65  66  74  62  70  69  67  64  71  68  64  63  71  69 100  68  62
##   [91]  68  66  64  67  65  65  69  63  72  76  69  67  69  63  67  66  79  64
##  [109]  73  63  65  73  70  68  71  64  68  69  NA  67  68  64  66  63  66  66
##  [127]  67  65  68  68  65  71  65  64  72  65  66  61  68  69  71  70  68  67
##  [145]  68  68  72  65  66  65  67  NA  69  66  69  67  66  71  70  71  66  67
##  [163]  66  72  68  69  71  70  67  69  65  65  64  63  69  64  72  63  64  64
##  [181]  67  71  70  61  67  72  66  70  67  67  71  66  68  74  64  65  66  66
##  [199]  68  78  67  74  74  62  66  69  68  89  66  68  67  75  60  66  73  68
##  [217]  62  62  65  69  64  67  70  70  69  61  69  63  67  66  63  68  65  67
##  [235]  68  64  71  69  67  65  68  67  67  66  70  65  69  65  63  67  61  65
##  [253]  66  66  69  63  65  67  69  65  65  65  67  72  NA  65  69  68  64  59
##  [271]  68  60  62  67  68  64  65  65  63  70  66  66  63  66  65  NA  67  66
##  [289]  63  NA  67  71  67  69  67  72  70  67  64  67  69  63  68  70  66  68
##  [307]  67  69  66  68  69  70  74  70  66  69  64  62  70  68  65  NA  71  66
##  [325]  61  67  65  65  NA  62  60  61  67  70  69  66  64  68  67  64  65  66
##  [343]  68  66  63  63  74  70  66  63  67  71  NA  72  68  66  70  66  72  61
##  [361]  62  68  68  63  70  68  72  67  61  69  75  NA  65  75  64  70  67  63
##  [379]  67  86  67  63  66  67  NA  66  64  73  68  70  67  62  68  72  69  66
##  [397]  70  71  65  70  65  62  62  70  66  67  72  66  68  62  64  65  66  67
##  [415]  69  68  64  68  64  71  61  68  64  72  NA  68  NA  66  63  74  63  72
##  [433]  69  67  66  64  67  69  64  65  72  66  66  67  69  73  69  68  61  63
##  [451]  68  63  65  68  66  66  70  61  71  70  69  61  68  74  67  70  64  66
##  [469]  63  61  68  65  69  68  69  70  68  67  67  75  70  70  64  59  63  67
##  [487]  68  68  97  66  61  70  65  64  69  64  61  64  68  67  62  66  72  71
##  [505]  65  68  65  64  65  65  73  72  64  69  69  70  83  68  84  75  67  69
##  [523]  66  65  70  66  74  68  68  62  71  63  69  71  66  64  65  69  66  67
##  [541]  65  65  67  66  69  70  68  70  67  72  69  69  64  63  70  70  66  70
##  [559]  66  68  61  NA  69  72  65  74  62  65  68  71  NA  65  68  70  63  63
##  [577]  69  66  70  63  72  63  65  NA  80  68  64  73  66  66  66  59  68  67
##  [595]  64  65  68  70  NA  72  62  68  73  69  67  65  63  66  66  70  69  70
##  [613]  58  67  66  70  67  60  65  63  72  NA  70  70  64  64  72  66  66  71
##  [631]  66  64  66  62  70  69  65  70  70  67  69  62  67  65  65  69  63  66
##  [649]  67  69  67  70  67  70  65  63  NA  69  60  69  72  63  63  70  NA  69
##  [667]  72  67  68  70  68  69  68  66  72  67  70  73  73  60  67  69  65  65
##  [685]  64  67  65  64  67  70  63  71  68  67  67  68  66  68  70  67  67  62
##  [703]  67  70  72  70  94  66  69  68  71  69  67  64  63  66  69  64  62  70
##  [721]  67  68  62  68  64  64  66  72  72  66  NA  69  72  69  69  62  70  68
##  [739]  68  70  65  73  66  71  62  68  70  68  70  72  69  63  62  68  69  68
##  [757]  65  59  66  63  72  NA  94  70  66  69  64  63  71  65  68  64  64  67
##  [775]  66  NA  66  71  71  68  64  67  64  68  62  64  68  69  65  67  71  65
##  [793]  65  65  68  68  67  65  66  63  72  67  67  66  66  69  62  66  64  67
##  [811]  71  68  66  75  72  68  68  69  63  70  66  66  71  72  69  71  69  68
##  [829]  NA  68  72  70  73  67  65  68  65  NA  66  67  70  NA  69  62  68  67
##  [847]  68  69  62  75  65  63  66  71  66  NA  66  68  71  68  68  62  65  71
##  [865]  63  68  69  69  71  71  62  NA  70  71  69  65  71  68  64  67  NA  71
##  [883]  62  67  66  NA  65  64  65  68  72  64  62  69  64  61  72  66  69  65
##  [901]  64  66  62  66  70  75  67  66  NA  NA  72  65  67  63  62  69  70  63
##  [919]  71  63  71  63  65  66  66  66  66  67  68  68  69  64  67  63  64  66
##  [937]  65  68  66  71  74  65  68  68  72  NA  61  65  63  66  66  73  63  73
##  [955]  63  65  65  66  65  70  68  64  68  62  61  69  65  65  NA  70  65  69
##  [973]  65  69  65  72  70  64  67  69  70  65  69  74  66  72  75  70  63  65
##  [991]  64  NA  NA  67  67  68  65  61  63  80  69  NA  70  65  68  64  69  89
## [1009]  67  92  67  70  68  70  67  69  67  69  63  66  68  69  66  72  62  67
## [1027]  67  67  65  67  66  70  71  64  72  60  71  71  NA  74  64  68  66  64
## [1045]  65  69  63  65  62  67  64  61  65  70  59  75  67  64  72  76  69  65
## [1063]  72  69  71  64  74  68  66  65  67  69  66  67  64  67  NA  68  66  66
## [1081]  63  66  66  65  69  71  66  66  65  71  69  61  70  70  65  64  68  63
## [1099]  71  58  68  65  65  68  69  71  65  64  75  67  68  NA  67  72  69  68
## [1117]  70  69  63  61  66  73  67  72  69  69  63  67  63  66  62  68  65  59
## [1135]  72  63  68  61  65  68  61  67  66  75  68  65  NA  64  67  63  67  65
## [1153]  62  69  70  68  68  64  63  68  67  68  66  67  69  70  68  66  67  65
## [1171]  67  63  64  64  66  68  67  72  67  66  66  67  65  70  69  69  66  66
## [1189]  67  67  67  72  68  70  69  65  72  69  68  62  60  67  67  67  63  71
## [1207]  66  65  69  63  64  67  62  68  66  69  71  66  70  65  64  63  63  66
## [1225]  68  74  71  67  66  67  62  68  62  82  70  NA  64  66  68  64  61  69
## [1243]  64  67  67  65  68  67  64  70  69  66  69  66  73  66  69  70  71  70
## [1261]  69  63  NA  73  68  69  76  68  65  65  69  66  69  59  65  NA  64  69
## [1279]  70  67  67  NA  68  72  65  NA  75  65  63  71  66  69  68  71  77  70
## [1297]  66  NA  NA  NA  66  72  NA  63  72  71  72  65  67  68  66  71  70  68
## [1315]  72  66  65  62  69  65  69  69  75  70  74  65  63  74  67  71  68  69
## [1333]  71  66  65  66  65  67  70  63  64  71  68  72  71  64  64  66  68  65
## [1351]  67  64  70  65  65  68  61  69  64  69  67  NA  66  72  73  73  63  69
## [1369]  71  63  69  72  68  62  68  71  67  65  68  59  71  70  62  62  68  68
## [1387]  61  67  65 101  65  67  NA  NA  64  67  69  67  62  66  72  67  66  67
## [1405]  67  68  63  NA  65  65  70  73  73  68  63  62  69  66  68  67  65  70
## [1423]  64  65  67  62  66  68  64  69  67  61  70  65  66  66  69  67  71  68
## [1441]  67  63  64  73  69  65  70  67  67  NA  69  68  NA  67  71  68  66  64
## [1459]  71  61  67  65  66  68  66  63  66  73  88  67  69  67  64  64  65  68
## [1477]  77  63  69  70  73  NA  71  66  71  66  63  70  66  66  66  62  69  63
## [1495]  68  NA  69  71  71  66  72  70  71  65  65  68  70  70  72  65  65  71
## [1513]  64  65  73  72  65  66  66  68  67  65  64  70  63  65  67  71  73  67
## [1531]  72  71  72  68  65  68  67  66  64  65  69  68  69  70  65  71  68  70
## [1549]  72  NA  64  NA  NA  71  69  67  66  71  63  62  NA  66  72  67  65  66
## [1567]  68  69  68  61  68  64  67  68  61  66  64  67  64  72  62  63  70  69
## [1585]  64  66  67  71  70  69  64  70  69  60  65  67  66  68  58  67  62  69
## [1603]  73  66  67  71  NA  74  67  68  61  65  71  61  70  70  69  70  67  63
## [1621]  70  61  64  65  65  66  66  63  66  64  65  62  71  63  70  70  65  68
## [1639]  68  NA  71  68  67  72  68  60  68  NA  67  70  70  68  67  62  66  69
## [1657]  66  64  66  63  62  65  68  65  63  68  72  69  66  68  64  61  67  68
## [1675]  74  67  64  69  63  67  65  67  62  70  67  NA  65  69  64  74  64  64
## [1693]  67  63  68  66  68  68  69  71  65  67  65  65  80  74  59  69  66  66
## [1711]  65  67  69  68  73  71  67  67  66  63  65  NA  69  67  66  66  69  63
## [1729]  64  64  69  73  62  62  66  68  66  NA  62  NA  67  65  69  67  64  62
## [1747]  71  72  74  66  72  65  70  62  65  70  69  70  66  73  69  66  65  70
## [1765]  70  67  68  68  61  70  65  66  67  69  69  67  66  63  67  64  68  65
## [1783]  65  70  62  68  62  68  70  NA  73  68  68  69  63  74  61  69  64  63
## [1801]  68  72  69  70  63  62  72  69  66  71  62  68  63  66  NA  69  68  69
## [1819]  67  73  71  71  68  70  71  NA  63  71  69  71  68  68  66  67  59  66
## [1837]  64  NA  69  69  61  62  61  63  71  NA  68  67  70  64  71  71  67  63
## [1855]  66  70  70  67  69  66  67  65  72  68  72  76  65  68  65  66  63  63
## [1873]  66  72  64  67  66  68  65  71  62  69  65  70  70  70  69  NA  69  73
## [1891]  65  62  67  65  65  70  70  71  71  NA  65  84  68  70  68  67  69  68
## [1909]  59  67  NA  63  64  NA  66  67  66  66  68  66  68  65  67  64  59  60
## [1927]  65  66  65  69  62  60  68  64  73  64  63  65  65  67  66  65  66  66
## [1945]  70  71  70  68  NA  68  66  67  66  69  67  61  70  70  70  64  65  70
## [1963]  62  64  67  62  72  69  72  68  64  72  73  67  64  NA  67  68  71  NA
## [1981]  59  68  64  70  65  72  66  68  62  70  70  64  76  67  68  67  69  67
## [1999]  73  71  70  73  65  70  66  64  68  70  72  66  74  67  NA  60  69  71
## [2017]  66  65  60  69  69  67  65  70  71  73  70  67  67  65  68  74  68  61
## [2035]  67  66  69  62  71  71  72  69  67  NA  68  69  65  70  65  67  72  69
## [2053]  69  NA  67  65  70  63  71  64  69  69  70  64  70  74  69  73  66  67
## [2071]  76  61  68  63  67  66  62  67  66  63  64  67  66  68  NA  68  63  62
## [2089]  72  69  67  65  69  NA  70  91  65  62  65  NA  67  72  60  69  61  70
## [2107]  68  75  75  72  66  71  70  63  72  65  71  65  69  71  68  66  60  68
## [2125]  67  71  74  70  63  64  66  64  69  NA  64  65  69  68  68  68  65  65
## [2143]  66  66  71  68  65  63  66  71  65  68  66  64  70  70  71  70  70  66
## [2161]  64  66  68  61  72  66  68  61  67  66  74  66  67  71  66  71  72  66
## [2179]  62  66  69  69  69  64  68  63  64  69  71  67  66  67  NA  69  NA  66
## [2197]  63  67  66  66  67  66  69  72  60  68  72  64  65  76  59  67  NA  64
## [2215]  67  69  69  67  72  NA  62  69  68  99  70  68  67  66  66  62  72  68
## [2233]  66  68  75  67  65  68  67  67  73  67  71  67  68  68  NA  68  63  68
## [2251]  74  69  70  65  65  68  68  66  70  66  64  70  68  74  71  61  64  64
## [2269]  73  62  71  68  71  72  66  67  66  68  64  66  69  65  72  65  70  64
## [2287]  62  69  62  69  NA  NA  64  63  69  68  NA  64  66  71  72  NA  66  65
## [2305]  NA  62  68  65  62  74  NA  70  65  66  67  73  65  NA  66  67  58  71
## [2323]  63  73  NA  68  66  78  68  77  65  73  64  67  69  60  66  70  66  64
## [2341]  70  64  72  70  62  66  65  64  NA  71  68  68  65  64  75  61  68  NA
## [2359]  71  66  66  70  62  72  72  63  69  68  67  71  67  62  69  67  87  62
## [2377]  64  74  69  65  66  70  68  70  68  69  66  NA  71  66  61  NA  63  73
## [2395]  68  70  68  68  71  68  70  NA  69  73  72  67  69  68  64  71  68  70
## [2413]  72  65  70  69  64  67  65  62  68  68  68  68  NA  72  69  68  71  69
## [2431]  71  65  68  60  NA  66  66  62  61  69  69  74  62  67  69  66  NA  69
## [2449]  65  72  69  61  63  63  68  68  65  71  64  65  67  67  67  87  67  72
## [2467]  69  65  66  70  71  67  72  63  67  72  72  NA  67  68  70  67  69  74
## [2485]  63  72  71  69  62  NA  68  67  71  70  NA  60  69  71  NA  73  68  67
## [2503]  74  NA  69  69  68  66  69  68  65  71  61  63  66  69  71  73  72  73
## [2521]  65  71  65  67  69  63  68  70  64  64  68  65  66  70  66  69  64  64
## [2539]  69  67  63  67  65  64  68  64  70  70  69  70  65  70  63  74  70  66
## [2557]  68  67  66  66  69  67  69  66  64  61  61  70  65  67  69  63  66  73
## [2575]  68  74  70  68  67  65  66  64  72  70  60  68  71  68  67  70  65  60
## [2593]  65  70  69  64  67  NA  74  67  66  69  64  NA  66  65  67  67  68  65
## [2611]  66  65  71  63  70  70  67  68  63  70  69  66  70  68  70  67  64  62
## [2629]  NA  62  66  64  72  NA  65  65  70  68  57  59  64  67  60  67  71  67
## [2647]  69  68  59  75  59  71  71  66  69  65  NA  68  88  66  67  63  68  65
## [2665]  67  67  67  64  65  70  67  68  65  63  72  68  71  70  68  68  68  71
## [2683]  70  67  61  64  67  65  66  62  70  64  70  66  62  63  66  58  70  63
## [2701]  65  NA  73  82  71  73  65  67  67  69  61  64  64  68  62  70  67  70
## [2719]  65  65  70  72  65  71  71  72  64  72  71  66  71  67  69  67  62  67
## [2737]  NA  NA  69  70  NA  65  66  68  72  65  60  63  73  71  59  70  63  67
## [2755]  65  64  71  NA  63  68  67  66  63  65  66  65  65  63  65  62  66  71
## [2773]  64  67  68  63  64  74  68  68  69  61  69  NA  67  63  68  68  67  69
## [2791]  64  67  70  72  NA  62  67  64  64  70  68  NA  65  59  69  67  68  62
## [2809]  65  69  65  68  68  71  71  66  66  66  65  66  67  66  69  66  64  70
## [2827]  NA  67  60  66  72  63  69  NA  69  68  66  63  70  68  68  67  67  69
## [2845]  68  67  70  70  NA  61  68  64  66  73  66  65  68  69  72  63  65  69
## [2863]  62  66  69  67  94  71  66  71  66  60  60  66  67  67  64  66  68  70
## [2881]  NA  86  73  61  68  70  71  71  68  70  70  62  67  68  68  64  69  70
## [2899]  73  66  68  68  66  62  67  73  65  70  68  67  66  65  66  66  60  NA
## [2917]  72  68  67  62  69  NA  64  65  75  69  65  60  69  65  67  70  66  69
## [2935]  69  68  70  66  65  65  65  69  69  65  NA  72  67  74  66  66  66  71
## [2953]  66  69  69  68  64  73  66  67  63  61  71  61  62  74  65  NA  66  76
## [2971]  67  71  65  68  68  67  64  60  73  69  70  64  64  65  62  72  64  67
## [2989]  64  61  72  70  70  71  68  68  70  73  69  71  64  NA  69  70  66  65
## [3007]  66  61  71  60  66  61  68  68  65  65  60  67  65  70  64  68  69  NA
## [3025]  65  65  68  66  65  71  68  62  61  70  62  65  68  70  68  69  73  71
## [3043]  63  66  67  66  69  72  NA  67  64  68  71  67  67  64  63  72  63  67
## [3061]  68  64  65  68  66  73  68  72  70  66  66  66  65  71  66  63  58  61
## [3079]  65  67  67  62  86  71  70  71  71  70  67  60  73  NA  62  67  61  61
## [3097]  60  68  65  67  67  74  64  64  67  74  69  62  69  68  74  68  73  70
## [3115]  68  64  71  65  68  67  NA  63  68  66  67  68  72  70  62  69  61  58
## [3133]  63  71  70  64  63  63  71  65  68  70  68  69  70  67  69  67  67  NA
## [3151]  63  67  70  71  74  70  59  64  67  63  66  62  65  73  70  62  NA  96
## [3169]  66  69  70  73  69  71  65  62  65  68  65  67  68  66  62  65  70  68
## [3187]  72  NA  63  67  69  NA  67  69  63  65  58  70  66  63  62  69  66  68
## [3205]  62  64  65  65  65  70  71  65  68  73  64  71  70  68  68  68  59  74
## [3223]  62  64  76  70  69  74  62  70  71  68  66  67  71  74  65  60  69  65
## [3241]  69  70  65  57  68  67  70  68  62  67  66  60  75  67  71  63  67  68
## [3259]  65  72  61  60  72  NA  67  71  66  70  64  66  NA  67  67  64  61  99
## [3277]  NA  72  66  64  69  65  66  73  66  65  71  58  69  63  66  69  69  63
## [3295]  65  76  67  70  60  68  68  68  69  62  64  71  68  72  64  73  69  70
## [3313]  69  64  66  69  NA  65  62  75  60  63  66  67  68  72  66  63  71  67
## [3331]  NA  66  68  66  68  68  66  66  70  68  65  70  66  68  64  65  NA  66
## [3349]  68  70  65  65  68  67  72  70  72  71  64  69  NA  70  68  71  71  NA
## [3367]  68  70  72  66  65  66  65  72  68  68  67  68  67  NA  65  70  64  66
## [3385]  64  66  67  68  71  67  69  67  61  68  67  64  63  72  69  66  64  61
## [3403]  63  65  71  78  65  66  66  74  62  66  71  67  69  72  72  65  71  64
## [3421]  69  65  69  64  69  68  NA  66  66  67  62  66  68  68  63  66  72  70
## [3439]  63  65  65  66  68  64  66  68  64  62  67  65  59  66  NA  63  68  66
## [3457]  NA  66  69  64  68  66  68  62  68  69  70  65  68  67  64  66  67  63
## [3475]  69  70  70  65  NA  67  61  70  68  64  68  68  65  69  63  69  61  69
## [3493]  62  58  71  NA  68  61  67  72  71  67  68  64  73  65  67  63  63  69
## [3511]  68  68  69  73  66  68  65  67  70  64  69  71  68  68  66  70  65  NA
## [3529]  70  67  63  64  60  62  65  69  66  72  68  69  65  65  70  67  73  70
## [3547]  66  68  61  70  66  67  69  64  65  75  63  69  68  66  66  66  68  65
## [3565]  70  68  70  61  64  71  72  66  63  62  66  72  68  NA  70  73  67  65
## [3583]  NA  65  70  66  65  68  66  71  65  70  69  67  82  66  66  65  61  72
## [3601]  70  71  84  72  70  62  71  62  68  74  68  NA  65  66  68  67  63  71
## [3619]  63  66  67  66  70  71  68  64  66  72  68  70  64  71  72  71  63  68
## [3637]  63  66  NA  NA  70  65  67  66  69  73  66  70  68  65  67  71  70  61
## [3655]  69  63  67  65  63  67  66  72  68  67  NA  66  73  71  65  65  65  68
## [3673]  70  NA  62  66  65  71  61  63  67  70  73  69  61  64  61  63  65  NA
## [3691]  68  72  62  58  68  74  68  67  65  63  71  62  65  66  71  68  72  66
## [3709]  66  67  71  72  64  60  NA  68  62  68  60  72  65  63  66  65  65  67
## [3727]  65  67  66  71  64  61  65  61  69  71  70  62  73  66  66  66  66  65
## [3745]  67  76  66  63  71  63  63  66  72  70  62  69  66  64  NA  67  71  69
## [3763]  70  70  61  NA  67  70  68  69  65  68  67  70  68  69  70  67  70  74
## [3781]  63  72  62  71  68  72  64  64  63  66  71  70  67  73  64  65  62  64
## [3799]  67  74  63  64  64  70  71  63  65  70  65  68  72  67  65  66  67  65
## [3817]  68  68  69  71  64  64  67  70  66  70  70  64  71  63  72  72  63  67
## [3835]  67  64  69  NA  71  70  98  65  63  61  67  64  65  73  69  67  NA  67
## [3853]  66  64  68  66  65  65  67  68  63  70  68  NA  NA  69  65  61  65  67
## [3871]  66  69  NA  68  65  64  68  64  70  68  NA  61  66  75  71  69  62  65
## [3889]  61  69  66  64  69  78  68  68  68  69  68  80  NA  64  64  68  65  66
## [3907]  67  64  66  63  71  62  64  72  NA  67  65  63  65  67  67  64  69  60
## [3925]  70  66  66  68  72  64  64  64  72  66  68  95  64  NA  68  67  67  71
## [3943]  63  66  65  68  68  62  67  NA  71  71  61  70  NA  70  67  66  63  65
## [3961]  75  66  61  65  61  73  63  67  62  71  70  70  69  66  72  63  65  71
## [3979]  66  69  62  66  66  64  68  68  67  68  65  NA  85  64  68  NA  65  63
## [3997]  64  62  68  63  68  63  68  62  67  66  65  69  64  75  66  62  70  NA
## [4015]  66  65  68  68  62  66  68  69  67  74  61  64  69  66  61  71  71  69
## [4033]  66  68  71  66  94  68  66  70  68  64  69  59  70  72  64  63  67  62
## [4051]  69  66  66  63  62  58  67  68  67  67  62  66  65  67  69  67  69  62
## [4069]  67  63  66  71  68  67  71  65  64  69  68  67  71  64  NA  69  67  58
## [4087]  66  69  70  70  70  66  61  71  NA  69  74  71  68  69  63  67  NA  66
## [4105]  69  68  63  69  66  71  68  69  65  68  67  65  65  64  69  64  66  65
## [4123]  69  66  64  61  72  67  63  69  70  71  60  70  69  63  69  71  68  64
## [4141]  68  69  65  68  74  72  67  73  68  70  62  67  69  93  68  69  68  64
## [4159]  69  66  68  72  63  NA  65  65  68  70  65  66  66  NA  64  66  63  68
## [4177]  68  65  69  66  72  NA  67  68  71  73  68  69  69  63  62  70  66  62
## [4195]  64  63  71  67  67  67  71  93  72  71  63  65  61  66  61  67  64  69
## [4213]  70  73  63  64  69  69  67  62  66  68  71  66  NA  68  59  70  66  65
## [4231]  66  73  65  65  NA  74  68  65  72  71  69  67  71  68  69  68  73  69
## [4249]  58  65  58  66  NA  67  67  65  71  66  68  65  71  NA  72  69  70  66
## [4267]  NA  62  66  70  73  70  71  NA  64  66  82  68  67  68  69  63  66  68
## [4285]  71  69  70  70  NA  68  65  72  67  68  69  70  69  68  65  70  65  61
## [4303]  69  67  65  63  67  76  70  67  66  65  65  63  72  68  62  65  69  61
## [4321]  67  66  70  72  69  68  74  70  67  68  69  66  68  69  66  NA  66  64
## [4339]  63  68  65  65  68  62  67  73  69  65  66  73  72  72  61  69  66  74
## [4357]  66  66  72  70  67  71  63  NA  64  65  65  62  65  64  NA  67  66  NA
## [4375]  68  58  65  68  64  66  92  69  68  63  64  68  67  68  66  68  64  63
## [4393]  62  66  65  66  66  69  67  NA  73  66  61  NA  67  66  69  69  67  65
## [4411]  63  63  66  66  69  72  70  68  66  67  68  62  64  71  65  69  65  71
## [4429]  69  65  66  68  72  74  64  64  63  66  67  64  62  71  63  72  71  61
## [4447]  71  69  61  68  67  70  69  72  66  67  70  68  68  65  63  62  66  62
## [4465]  61  63  64  74  70  68  69  62  71  69  68  65  65  72  63  72  66  71
## [4483]  67  61  70  68  70  65  65  65  65  66  62  63  63  70  67  66  63  66
## [4501]  67  68  67  66  71  69  72  70  68  68  67  62  67  69  64  66  69  70
## [4519]  69  72  61  NA  68  NA  65  66  67  68  67  63  64  66  69  70  72  63
## [4537]  68  67  69  69  71  67  64  68  67  62  68  72  61  67  70  59  70  60
## [4555]  74  68  67  67  63  62  64  68  65  71  68  68  68  67  NA  70  69  70
## [4573]  69  59  64  70  63  66  72  71  62  62  64  65  68  67  61  68  68  62
## [4591]  62  74  68  66  65  66  67  76  66  68  63  65  63  59  74  62  59  71
## [4609]  73  68  68  66  69  70  74  75  71  71  65  NA  65  67  67  71  72  62
## [4627]  70  72  64  66  69  71  68  71  66  68  61  71  70  66  61  67  72  65
## [4645]  68  70  63  69  62  71  64  71  72  66  69  60  68  65  67  66  68  63
## [4663]  NA  66  67  66  60  67  NA  70  69  68  67  63  70  71  67  64  66  70
## [4681]  65  68  65  65  69  70  64  62  73  62  62  72  67  68  65  79  66  68
## [4699]  65  67  67  68  72  65  65  70  68  63  68  69  NA  64  69  62  65  70
## [4717]  72  66  70  67  65  68  68  69  72  65  63  68  62  69  65  65  70  59
## [4735]  63  64  63  67  65  64  65  72  72  66  62  68  67  69  67  63  65  71
## [4753]  70  68  65  68  69  NA  62  72  64  58  66  64  68  69  71  71  62  70
## [4771]  63  66  65  69  63  64  66  67  66  65  72  70  67  72  65  62  67  64
## [4789]  72  66  70  66  67  NA  72  68  64  66  68  66  NA  70  69  69  66  68
## [4807]  71  64  67  68  68  69  71  68  65  63  65  72  67  69  67  64  62  71
## [4825]  64  69  65  73  64  64  70  70  64  74  69  67  73  66  67  75  73  67
## [4843]  65  71  63  68  72  NA  67  66  72  64  68  65  74  65  63  65  70  71
## [4861]  66  NA  67  64  67  NA  70  71  68  65  70  67  63  65  70  67  60  65
## [4879]  64  67  71  69  70  69  63  67  66  69  69  72  65  63  69  69  64  69
## [4897]  72  62  66  65  65  67  63  66  61  64  65  68  69  61  72  61  66  60
## [4915]  69  72  69  71  64  71  64  67  67  66  73  73  70  70  62  68  65  73
## [4933]  66  64  63  62  70  NA  64  70  62  67  66  74  69  70  68  71  73  69
## [4951]  61  68  66  67  64  67  61  62  69  61  69  64  65  64  68  67  68  61
## [4969]  69  64  74  66  68  65  66  66  65  67  65  63  67  70  68  66  NA  72
## [4987]  68  66  62  67  62  67  68  66  68  62  68  62  69  62  71  69  66  64
## [5005]  65  NA  69  68  71  66  65  72  67  67  70  64  65  68  67  66  69  64
## [5023]  68  68  65  65  65  67  63  62  73  72  71  67  66  68  70  66  56  71
## [5041]  64  NA  70  70  71  70  62  72  62  67  NA  60  72  66  66  69  70  70
## [5059]  70  67  67  59  68  71  61  63  67  70  69  66  70  67  61  74  70  66
## [5077]  73  65  64  63  69  NA  65  NA  69  71  68  70  71  68  69  71  63  66
## [5095]  67  71  59  66  72  70  68  63  69  75  67  74  66  65  60  63  69  68
## [5113]  65  74  65  61  67  66  69  65  65  66  73  64  67  67  68  71  64  67
## [5131]  68  67  70  64  63  71  64  70  70  67  62  NA  69  NA  70  69  65  66
## [5149]  69  66  65  66  72  62  64  61  70  67  66  66  68  67  65  70  68  61
## [5167]  65  71  66  61  67  66  71  62  67  64  68  67  63  70  67  71  62  75
## [5185]  72  73  64  66  69  70  70  71  64  71  63  68  71  66  72  65  60  67
## [5203]  65  64  72  62  67  67  69  65  62  69  72  63  64  67  70  64  69  72
## [5221]  69  75  67  67  64  68  65  70  57  69  70  63  66  64  62  71  64  72
## [5239]  64  71  68  68  68  69  67  66  65  63  62  67  65  66  64  67  67  61
## [5257]  66  66  67  64  67  68  64  63  68  64  70  64  59  71  67  73  66  73
## [5275]  62  69  66  NA  65  67  64  67  66  NA  68  64  63  72  75  71  66  71
## [5293]  NA  NA  58  62  69  65  69  68  70  72  66  68  67  61  64  74  64  64
## [5311]  61  71  72  68  69  74  70  69  64  71  65  71  66  64  NA  71  65  59
## [5329]  63  64  63  70  70  NA  65  71  70  66  64  64  59  65  NA  67  62  70
## [5347]  75  66  65  64  70  71  68  64  67  65  62  68  66  68  NA  68  66  70
## [5365]  60  69  65  NA  64  71  66  66  68  NA  66  61  70  68  65  69  67  62
## [5383]  61  65  65  66  NA  69  70  63  64  65  71  61  69  69  66  72  60  62
## [5401]  66  69  69  71  57  72  66  70  67  65  68  63  63  68  60  67  65  68
## [5419]  62  65  66  67  60  74  62  61  NA  66  NA  72  70  71  64  70  68  61
## [5437]  68  64  64  NA  72  66  74  65  64  69  62  62  72  73  64  65  70  66
## [5455]  70  69  64  63  66  68  97  71  66  72  70  69  66  69  65  75  70  70
## [5473]  69  73  74  66  74  67  67  70  67  80  70  71  64  68  68  69  72  65
## [5491]  64  64  58  69  61  68  66  68  70  62  71  61  NA  65  63  74  68  65
## [5509]  66  69  69  70  70  71  72  61  68  66  70  NA  62  69  69  64  63  69
## [5527]  61  70  64  76  73  69  72  70  73  68  66  67  67  62  72  65  69  69
## [5545]  69  69  69  70  67  69  75  66  63  64  66  72  71  70  67  65  65  73
## [5563]  66  NA  71  66  65  75  74  65  71  65  65  67  66  67  66  65  59  63
## [5581]  65  61  68  65  72  59  63  69  70  67  66  68  71  69  66  66  74  66
## [5599]  72  69  68  71  61  65  71  59  71  72  71  67  67  74  63  68  NA  66
## [5617]  67  70  65  68  70  66  69  65  68  65  70  NA  NA  64  70  64  67  68
## [5635]  67  66  66  67  NA  NA  68  67  69  64  67  67  67  67  68  65  70  68
## [5653]  72  67  66  68  75  66  67  71  68  65  67  66  60  NA  64  72  60  NA
## [5671]  62  70  65  77  71  66  74  70  NA  64  NA  68  63  61  61  65  69  69
## [5689]  65  72  69  71  67  72  70  68  66  68  71  70  65  65  68  69  66  62
## [5707]  70  65  71  68  65  70  69  66  67  63  70  65  70  74  68  64  73  66
## [5725]  66  67  67  69  69  68  64  70  67  68  67  73  65  69  63  68  64  68
## [5743]  66  65  69  69  74  64  63  64  71  NA  72  67  64  70  65  69  65  66
## [5761]  67  68  65  68  63  65  61  68  65  66  65  NA  70  70  67  75  65  66
## [5779]  62  64  60  70  72  67  67  72  63  60  NA  72  70  71  66  NA  73  71
## [5797]  64  66  69  66  63  62  98  71  66  75  68  69  68  60  64  71  69  60
## [5815]  70  66  68  67  69  75  65  65  66  64  70  63  66  71  68  68  71  63
## [5833]  NA  73  68  70  66  72  70  68  60  68  74  68  72  69  98  68  70  64
## [5851]  65  67  65  70  68  65  74  65  68  74  67  64  66  61  73  70  70  63
## [5869]  69  NA  68  65  68  69  66  58  67  65  62  65  69  70  70  63  69  64
## [5887]  69  70  64  65  70  60  68  61  68  61  64  66  70  65  74  66  65  69
## [5905]  69  66  63  69  65  67  67  65  69  NA  67  66  64  70  65  65  64  64
## [5923]  61  65  68  70  74  60  71  70  67  68  64  67  65  72  65  71  72  70
## [5941]  63  67  67  62  72  69  61  67  66  68  62  63  70  68  71  65  59  64
## [5959]  67  68  95  70  68  65  NA  67  69  68  72  71  75  70  66  67  70  71
## [5977]  64  65  64  62  64  66  64  71  NA  70  71  68  66  66  65  64  67  65
## [5995]  69  69  69  68  67  68  65  69  73  76  69  69  68  70  NA  73  64  65
## [6013]  62  64  69  67  65  63  66  70  70  67  65  66  66  72  64  71  70  64
## [6031]  70  67  NA  68  69  68  68  64
as.numeric(czynniki4$Sleep_Hours)
##    [1]  7  8  7  8  6  8 NA  6  6  8  6  8  8 NA  8 10  6  9  7  5  6  8  8  5
##   [25]  6  6  4  4  7  8  5  6  7  9  8  6  8  6  7  7  9  8  6  6  7  5  7  8
##   [49]  8  7  5  5  6  8  8  7 10  9  8  8 NA  4  5  7  7  7  7  4  8  7  7  8
##   [73]  7  7  6  4  5  7  7  7  6  5  7  7  8  6  4  4  6  7  7  6  5  4 NA  7
##   [97]  6  5  6  7  7  7  9  6  9  7  7  8  6  7  5  8  8  9  9  6  8  6  7 10
##  [121]  8  8  6  7 NA  9  7 NA  5  9  6  8  6  8 NA  9  8  6  8  8  5  5  5  5
##  [145]  8  8  4  6  5  8  6  5  7  8  6  7  6  9  6  6  7  7  8  9  9  6  7 NA
##  [169]  9  6  8  8  8  9 NA  6  8  7  4  5  8  8  5  9  7  5  6 NA  6  4  7  8
##  [193]  5  7  6  8  4  8  4  7  6 NA  5  9  5  5 10  7  5  7  4  6  7  9  7  7
##  [217]  6  9  8  8  7  5  9  7  7  8  7  5  7  7  9  4  7  8 NA  6  5  6  9  4
##  [241]  5  6  6  7  9  5  7  7  6  5  6  6  8  8  5  6  6 10  7  5  6  6  8  7
##  [265]  7  7  7  4  7  5 10  7  7  6  8  5  7  6  8  6  9  8  8  9  6  8  4  7
##  [289]  6  5  6  6  7  6  7  6  6  7  7  8  8  8  7  7  8  6  4  5  9  7  7  7
##  [313]  8 NA  7  8  6  8 NA  7  6  7  6  9  4  8  8  6  8  7  5  9  8  8  6  8
##  [337]  5  4  5 NA  6  6  6  4  7 NA  6  9  7  8 NA  8  7  5  6  7  4 NA 10  8
##  [361]  8  7  8  9  8  7  7  8  6  8  6  5  6 10  6 NA  6  7  4  5  6  5  7  5
##  [385]  7 NA  7  6  9  8 NA  6  8  9  8  5 NA  8  7  6  7  7 NA  8  6  7  9  7
##  [409]  8  5  8  8  6  7  7  8  6  7  9  9  8 NA  9  7  7  6  8  8  7  5  8  6
##  [433]  7  9  5  7 NA  7  7  8  7  8  7  7 NA  7  6  8  7  6  9  7  5  7  7  7
##  [457]  6 NA 10  4  5  6  6  5  6  7  5  8  5  8  8  6  5  8  6 NA  8  6  7  6
##  [481]  9  6  7  8  7  8  7  5  7 NA  7  9  4  8  6  6  9  7  6  8 NA  9 10  8
##  [505]  7  5  9 NA  8  8  7 NA 10  7  6  9  7  7  9  8  8 NA  5  6  7  7  8  8
##  [529]  5 10  7  9  4  7  5  6  7  6  9 10  6 NA  5  9  7  7  7  8  5  7  6  7
##  [553]  8  6  9  4  9  9  6  6  5  8  7  5 NA  6  7  7  6  6  8 NA  9  6  4  6
##  [577]  6  5  7  7  4  7  9  8  7  4  6  9  6  6  5  7  7  6 10  8  7  4  8 10
##  [601]  7  6  5  8  9  6  6  7  6  5  6  6  9  9  8 NA  6  9  8  5  6  5  4 NA
##  [625]  5  6  6  9  5  5  8  6  6  5  8  7  7  6  6  7  8  9  9  8  8  6  8  7
##  [649]  8  8  8  5  7  6  6 NA  7  4  8  9  8  7  9  6  7 10  5  5  8  7  6  5
##  [673]  4  5  9  7  4  9  9  9  6  7  7  8  9  7  8  7  7  6  5  6  6 NA  9  7
##  [697]  6  8  7  8  6  9  9  7  8  9  6  7  7  5  8  9  7  8  9  6  6  6  8  8
##  [721]  7  8  9  8  7  7  8  7  8  9  7  4 10  7  9 10  9  7 10  9 NA  6  4  8
##  [745]  9  8  4  5 10  7  9  5  7  7  6 10  7  5  5  8  6  6  8  4  6  5  6  7
##  [769]  7  7  9  7 NA 10  7 10  7  7 NA  7  9 10  4 NA  6  4  8  8  8  8  7  8
##  [793]  7  7  7  5  8  5 NA  7  5  6  6  9  7  8  9  9  7  6  8 NA  8  7  8  7
##  [817]  6  8  7 10  6  8  6  4  8  6  9  8  7  5  8  6  5  8  5  4  9  6  4  6
##  [841]  6  9  5  5  8  6 NA  6 NA NA  7  9  6  6  8  9  6  7  8  9  8  6 10 NA
##  [865]  7  8  8 10  7  7  9  7 NA  8  8  4  4 NA  7  7  7  8  8  8 NA  7  7  9
##  [889]  6  7  7  9  4  7  8 10  7  6 10  8  9  8  5  5  8  8  6  9  6  7  7  9
##  [913]  5  6  5 10  7  6 NA  8  8  6  5  7  9 NA  6  5  8 10  8  6  6 10  6  7
##  [937]  7  8  9  9  7  7  8  6 NA  7  8 10  8  7  6  7  5  4  8  8 NA  7  4  8
##  [961]  9  8  7 NA  6  7  7  6  7 NA 10  7  6 NA  9  9 10  7  8  5  6  5  8  7
##  [985]  7  6  4  7  7  4  8  7  8 10  7  8  9  8  6  5  8  6  9  6  7  5  6  6
## [1009]  6  7  6 10 NA  9  7  7  6 10  7  6 NA NA  9  6  6  9 10  7  9  5  6 NA
## [1033]  8  7  9  6  7  5  9  9  8  7  6  7  8 NA  9  9  6  7  6  6  9  7  7  7
## [1057]  7  6 NA  6  6  7 NA  6  8  7  7  8  4  6  8  7  7  6  9  8 NA  9  6  8
## [1081]  8  7  7  9  6  9  6  7  6 10  7  5  7  8  7  6  9  5  6  7  6  8 10  6
## [1105]  9  5  8  6  8  4  5  8  6  7 10 NA  8  6  7  5  6  7  7  8  8  5  6  4
## [1129]  6  8  9  7  9  8  7  6  4  9 NA  9 NA  7  6  7  7  7  6  6  9  6  4  5
## [1153] NA  7  6  9  8 10  6  7  9  8  6  8  8  6  7  9  8  6  6  8  4  6  9  7
## [1177]  6  5  8  7  7  8  7  7  5  5  8  8  8  6  8  6 NA  6  6 NA  8  7  7  6
## [1201]  7  7  6  7  7 10  6  6  7  6  5  5  6  6  7  4  8  6  8  8  6 NA  9  5
## [1225]  8 NA  9  6  6 NA  8  6  7  6  5  7  6  6  9  6 NA  9  6  7  8  8 10  6
## [1249]  5  8  7  7  6  6 NA  6  7 NA  5  5  6  9  6  5  6  5  8  5 NA  7  8  8
## [1273]  5  9  7 10  9  7 10  7 10  8  8 NA NA  8  7  7 NA  8  8  6  7  4  8 10
## [1297]  7  5  8  6  8  8 NA  7  8  7  6  8  5  7  5  6  6  9  9  9  6  8  7  7
## [1321]  4  8  7  8  8  6  7  5  9  8  6  8  7  6  7  8  8 10  7 NA  8  7  6  6
## [1345]  4  8  5  6  7 10  5 10  9  8  9  8  4  6  7  6  8  7  8  7  7  6  5  7
## [1369]  6  9  5 10  7 NA  6  8  7  7  8  9  6  7  7 10  7  8  8  8  6  6  7  4
## [1393]  7  6  7  7  5 NA  8  7  8  5  9  8  7 NA  9  6  5  6  7  7  9  6  6  5
## [1417]  8  5  8  6  6 10  9  7  5 10  7  7  8  4  7  7  5  7  7 10  9  7  7  9
## [1441]  7  5 10  6 10  8  6 NA  8  5  8 10  5  6  9  7  7  9  8  6 10  5  7  6
## [1465] NA  5  7  8  9  9  7  6  9  6  5  8  9  6  8  8  6  9  5  6  6  5  8  8
## [1489]  8  7  8  7  6  6  4  9  9 10  6  6 NA  8  9  6  8  9  8  5  7  4  5  5
## [1513]  7  7  7  5  7  8  8  8  8  8  8  5  5  6 NA  7  7  4  7  7  4  7  5  6
## [1537]  8  7  6  6  6  7  5  9  5  8  6  7  8  6  7  8  9  6  6  8  7  7  9  4
## [1561]  5  4  9  8  5  7 NA  4  7  5  8  5  7  9  8  8  7  5  6  7  7  5  8  5
## [1585]  9  7  8  8 10  7  6  9  5  7  7  8  5  7  7  5  7  7  6  6  5  8  9 10
## [1609]  8  6  6  7  7  7  9  6  9  7  6  6  7  8  6  8  6  7  5  8 NA  9  8  7
## [1633]  9  8  9  6  8  9  5  5  4  5  6  8  7  6  5  7  8  8 10 NA  7  7  7  6
## [1657]  4  5  8  7  8  8  8  8  7  7  4  6  6  7  6  8  6 NA  6  6  6  6  9  7
## [1681]  7  6  7  7  7  9  7  5  7  6  8  7  9  6  7  5  7  5  7  7  7  8  7  5
## [1705]  6  7  7  7  9  7  8  4 NA 10  9 NA 10  7  7  7 NA  4  8  7  7  7  9  8
## [1729]  7  7  6  7  8  7  7  8  5  6  5  7  8  9  9  6  7  6  9  9  7  6  4  5
## [1753]  5 10  5  6 10  7  8  7  4  9  8  7 10  6  7 NA NA  8  7  5  6  5  9  5
## [1777]  9  9  6  6  6  9  9  6  9  9  7  7  9  9  8  7  9 10  6  7  8  8  6  9
## [1801]  6  6  6  5  8  7  9  8  4  9 10  9  9 NA  6  7  8  8  6  6  5  8  6  7
## [1825] 10  8  7  8  9  5  6  7  6  7  5  8  6 NA  7  8  4  8  7  8  5  8  9  7
## [1849]  6  6  8  8  8  7 NA  7  6  8  7  9  9  7  8  6  7  8  5  8  6  6  6  7
## [1873]  5  7  7  6  5  8  5 10  8  8  7  6  6  5  7  9  5  9 NA  8  8  7  7  6
## [1897]  7  7 NA  8  7  7  6  6  8  6  6  6  6  9  7  7  7  5  9  8  8  8 10  6
## [1921]  5  8  5  7  7  8  6  6  8  6  7  9  7  9  7  6  8  4  8  6  8  7  5  6
## [1945]  7  7  8  8  8  8 NA 10  8  8 10  7  6  9  9  7 10  7  8  9  7  9  6  6
## [1969]  9  7  6  7  8  5  8  8  9  7  7  7  7 10  5  8  7  7  8  9  8  9  7  7
## [1993]  5 10  7  8  9  6  9  7  9  8  7  5  8  4  8  7  4  6  6 NA  9  9  6  6
## [2017] NA  7  6  6  6  6  9  8  8  9  8  9  8  7  8  7  5  4 10  6  6  9  5  8
## [2041] 10 10  6  7  6  7  9  5  8  7  9  9  6  7  8  8  4  8  9  7  8  9  7  8
## [2065]  7  7  6  7 10  6 NA  7  9  9  6  6  6  6 NA  6  6 NA  7  7  6  5  9  7
## [2089] 10  8 10  8  7  6  6  9  7  8  8  8  6  9  7  7  8  7  4  9  9  4  5 10
## [2113]  7  7  6  5  7  8  7  8 NA  6  7  9  6  7 10  6  9  7 10  5  7  5  6  6
## [2137]  7  5 NA  8  5  6 10  7  4  5  7  7 NA 10 10  7  8  8  9  6  8  7  7  7
## [2161]  5  4  7  6  8  8  7  9  7  5  7  9  4  7  8 10  9  7  8  4  5  7  7  7
## [2185]  7  7  5  7  5  6  7  8  7  6  5  6  7  8  8  5  8  5  8  8  4  8 NA  9
## [2209]  6  7  8  8  8  6  8  8  7  6  6  9  8  7  7  4  7  5  7  9 NA  7  8  6
## [2233]  7  8 NA  7  9  8  5  5  4  5  7  9  6  8  4 NA  6 10  4  4  6  4  6  7
## [2257]  7  5  9  8  8  5  9  9  7  8  7 NA  7  6  7  9  6  6 NA  7  8  8  7 10
## [2281]  7  8 10  8  6  7  7 NA  6  9  8  7 NA  7  8 10  4  8  7  7  4  8  7  6
## [2305]  7  7  4  7  8  6  7  9  7  8  7 10  6  6  7  6  5  8 NA  6  5  4  8  5
## [2329]  7  8  8  5 NA  9  6  6  8  5  7  8  5  6  9  7  8  8  7  5  6  7  5  5
## [2353]  9 NA NA  8  6  4  6  7  7  7  7  6  8  5  8  6 10  7  6  6  6  8  8  8
## [2377]  7  8  9  8  7  8  5 10  8  8  7  4  7  7  6  6  8  9  7  6  7  7  8  6
## [2401]  8  8  6  4  6  9  4  9  4  6  6 NA  7  7  6  8 NA  7  6  8  8  6  6  6
## [2425]  7  8  7  4  8  5  6  7  7  8  6  6  7 NA  8  7  9  9  8  5  8  7  6  6
## [2449]  7  6  7  7  8  7  6  4  8  7  7  9  5  7 NA  8  4 NA  8  6  7  6 NA  8
## [2473]  5  5  9 10  8  8  7  7  7  9  7  7  7  9  7  7  6  5  9  9  9  5  9 10
## [2497]  9  9  8  8  5  6  7  7  8  4  7  8  8  8  8  8  7  6 NA  8 10  8  8  5
## [2521]  7  7  8  8  8 10 NA  8  8 10  8  8  8  9  6 10  4  7  7  7  9  8  6  6
## [2545]  7  9  7  7  8  7  9  7  7 NA  8  7 NA 10  8 NA  7  7  8  4  4  9  7  6
## [2569]  5  7  7  9  8  7  8  9  8  8  7  6  5  5  8  8  9  8  9  7 NA  5  7  4
## [2593]  7  9  7  8  7  6  7  9  8  6  5  7  6  7  5  9  7  7  6  7  7  6  7  9
## [2617]  4  7  6  9  7  5  7  8 10  4  9  5  7 NA  7  7  9  8  7  7  8  9  8  9
## [2641]  6  9  8  6  7  7  7 NA  6  7  6  6  9  7 10  7  9  7  7  8 NA  7  7  6
## [2665]  7  8  7  7  7  7  8  7  7  8  7  7  7  5  7 10  6  6 10 NA  9  7  7  8
## [2689]  7 NA  4 NA NA 10  8 NA  9  6  6  4  6  8  9  5  7  4  7 10  4 NA  8  8
## [2713]  6  9  6  8  9  8  8  8  9  7  6  7  6  6  9  8  8  9  8 10  4  6  7  7
## [2737] 10  8  6  8  4  7  7  6  7  6  6  8  8  6  6  6  7  6  9  7  8  5  6  8
## [2761]  8  5  7  7  6  8  5  6  8  7  7  7  8  8  8  7  6  6  5  6  6  9  5  9
## [2785]  7  7  8  5  6  5  6 NA  9  6  4  6  8  9  7  6  7  8  5  7  7  7  7  6
## [2809]  8  7  7  5  8  6  9  5  4  4  4  8  7  9  7  7  7  6  6  5  8  7  7 10
## [2833]  6  7  7  9  7  7 10  6  7  8  6  8  6 NA  8  7  5 NA  7  8  7  8  8  7
## [2857]  7  7  6 NA  8  9  6  8  9  9  5 NA  4  5  9  6  5  9  5  9  5  5  7  6
## [2881]  7 10  7  9  7 NA  4  8  8  6 10  6  5  8  5  7  8 NA  6  9  5  8  8  7
## [2905]  7  6  6  7  8  9  4  4  9  7  7  7 10  8  6  6 NA NA  9  6  5  9  5  8
## [2929]  6  9  5  6  8  8  9  8  8  9  5  6  5  4  8  9  8  8  7  7 10  9  6  9
## [2953]  9  8  8  5  5  5 NA  6  8  8  8  6  7  8  8  6  7  7  6 NA  6  7  6  6
## [2977]  8  6 NA  8  7  7  7  8  7  7  5  7  9  6  5  8  8  6  7  7 NA  8  6  8
## [3001]  6  9 10  6  8  7  8  6  7  6  7  5  7  5 NA  7  8  8  8  5  9  6  6  7
## [3025]  8  8  6  7  7  8  6  6  5 NA  8  9 NA  4  7 10  6  7  5  7  7  5  5  5
## [3049]  6  8  6  9  6  7  8  9  6  8  6 10  5  8  9  5  8  6 10  4  5  5  5 NA
## [3073] 10  9  7  6  8  7  6  5  7  7  6  6  8  8 10 NA  5  7  5 NA 10  9  9  9
## [3097]  4  8  6  8 10  9  7  9  4  8  8  8  8  8  4  7  6  8  6 NA  5  7  7  8
## [3121]  7  9  7 NA  7 NA  5  5  9  6  7  7 NA  9  7  6  6  8  8  8  7  5  8  7
## [3145]  7  5  6  8  7  8  9  8  8  6  6  9  6  8 10  8  7  5  7  9  7  9  8  7
## [3169]  5  6  6  8  7  9  7  6  6  7  6  9  7  6  5  7  8  6  7  8  7  5  5  4
## [3193]  8  5  7  6  6  6  6  9  6  8  9 NA  8  6  7  6  7  5  8  5  7  6  8  7
## [3217]  5  8  7  7 10  9  7  5  5  9  6  5  8  9  9  6  8  7  8  7  6  9  7  6
## [3241]  7  6  8  7  6 10  5  8  7  5  6  5  7  7 10  6  9  8  4  6  8 NA  6  6
## [3265]  7 10  6  7  8  5  5  5  5  9  8  8  8  7  7 NA  5 10 NA  6  7 10  9  8
## [3289]  8  6  8  7 NA  9  7  5  6  8  9  8  8  7  7  7  7  6  8 NA  5  6  8  8
## [3313]  4  8  7  6  7  5  7  5  6  6  8 NA  8 NA  7  8  9  5  6  8  9  7  5  7
## [3337]  8  7  5  9  6  8  4 NA  6  8  5  7  9  6  9  8  9  7  7 10  8  7  8  6
## [3361]  7  9  7  6  6  7  6  5  5  9  7  7  6  6  6  7  5  9  7  7  8  8  6  8
## [3385]  8  7  9  8 NA  9  7  7  8  7  8  6  4  8  5 NA  8 NA  4  7  7  8  5 NA
## [3409]  8  6 10  6  7  5  7  4  7  9  5  5  9  5 10  8  9  6  9 NA  8  6  5  7
## [3433]  7  6  9 10  7  6 10  8  8  9  7  7  9  8  6  6  9  9 10  6  7  6 NA  7
## [3457]  8  6  4  5  7 10  6  7  8  6  6  7  6  4  6  9  9  6  6  6  7  6  7 NA
## [3481]  8  6  6  8  8  7  8 10  8 10  7  9  9  7  6  6  8  5  6  8  4  5 10  9
## [3505]  6  5  5  8 10 10  5  7  6 NA  5  6  6  8  6  8  9 10  8  7  9  9  8  5
## [3529]  9  8  6  6  8  4  7  6  6  5  9  4  7  6 10  7  4  8  5  8  8  9  7  8
## [3553]  7  6  9  5  7  6  8 NA  6  7  9  6  6  5  6  7  7 10  4 10  9  7  6  7
## [3577] 10  6  7  6  6  6  5  7  7  6  4  7  7  7  8  6  9  8  8 10  6  9  9  7
## [3601] 10  7  7  7  8 NA 10  6  4 10  9  8  6  8  5  7  7  8  5 NA  7  8  7  6
## [3625]  4  5  6  5  8  7 10 10  9  6  9  4  9  4  7  9  8  5  7  8  7  6  8 NA
## [3649]  7  9 NA  6  9  9  6  6 10  7  7  7  9 10  7 10  6  7  8  6 NA  6  5  4
## [3673]  7  8  5  7  7  7  6  7  7  8  5  5  7  6  7  6  9  9  8  8  7  7 10  6
## [3697]  5 NA  5  5  7  8  5  6  8  6  6  5  6  6  7  8  7  7  8  6  8  5  7  9
## [3721]  7  9  7 10  4  8  4  7  9  9  8  7  8 10  8  6  8  6  8  8  8  7  9  6
## [3745]  7  7  9  6  7  6  8  5  9  8  6  6  9  8  6  6  8  8  8  7  8  7  6  9
## [3769] NA  7  7  6  7  6  8  7  5  7  6  4  7  9  7  8  7  6  6  5  8  8  7  4
## [3793]  8  6  7  5  7  7  4  9  7  7  8 NA  8  5  4  7  9  5  6  4  7  8  8  6
## [3817]  4  5  9  8 NA  5  9  6  8  5  7  9  6  8  5  6  8 NA  8  6  5  6  9  6
## [3841]  9  7 10 10  9  5  4  7  8  8  6  5  8 10  6 10  7  7  8  7  9  6  7  5
## [3865] NA  5  8  5  8  6 10  9  8  5 NA  6  6  9  6  6  6  8  5  7  8  4  5  7
## [3889]  9  9  6  9  7  7  7  6  6  5  8  8  8  5  6  9  7  7  8  7 NA  8  5  9
## [3913]  6  8  7  6 NA  8  7 10  8 NA  9  8  9  6 NA  7  9 10  6  7  8  7  6  6
## [3937]  8  7  7  7  6  7  6  6  5  7  8  9  5  9  7  5  6  4  5 10  6  8  7  7
## [3961]  8  4  9  7  6  8  7  7  8  7  5  8  7  4 NA  6  8  6  5  9  8  7  8  8
## [3985]  5  7  9  7  8  7  9  9  9 10  8  8  6  6  7  5  7  8  5  7  7  7  8  8
## [4009]  9  8  9  7  7  7  9  7  7 10  5  8  7  7  6  6  6  8  8  4  5  8  8  5
## [4033] NA  8  6  5  7  7  7  6 10  6  6  7 NA  8  9  8  4 NA  9  9  8  6  7  6
## [4057]  5 NA 10  6  9  6  5  8  7  9  9  7  9  6  9  5  9  9  6  9  5  6  7  8
## [4081]  5 10  4  7  4  9  6  7  7  5  5  9  7  4  7  4  7  6  7  8  9  5  6  8
## [4105]  7  4  7  9  5  7  4  8  7  6  6  5  9  6  8  6 NA  9 10 10  6  6 10  7
## [4129] NA  6  6  8  4  8  8  6  7  7  7  8  6 10  7  7 10  4 10  7  6  5  6  7
## [4153]  8  7  6  9 10  9  6  8  8 NA  6  6  9  8  5  8 10  6  6  8  9  7  9  6
## [4177]  5  6  5  8  6  7 NA  7  7  9  5  8  8  7  6  5 10  7  7 10  7 10  5 NA
## [4201]  5  7  6  7  6  7  6  9  5  7  5  6  7  7  5  6  5  9  5 10  9  8  7  8
## [4225]  8  9  7  9  7 10  7  5  7  8 NA  4  8  8  5  7  7  8  6  6  5 10  8  6
## [4249]  5  5  7  4  8  8  7  7  8  7  8  5  8  7  9  7  7  6  9  4  8  7  7  7
## [4273]  8  6  7  8  6  8  8  6  5  6  7  7  9  6  6  8  6  6  6  4  8  8 NA 10
## [4297]  9  6  9  7  6  6 NA  7  9 NA  6  5  8  8  9  7  8  8  7  8  8  7 10 10
## [4321]  7  7 NA  7  9  5  7  8  9  5  6  6  5  7 NA  7  5  4  8  6  5  8  6  4
## [4345]  7  9  6  6 10  8 10  7  7  9  7  7 10  7  8  6  8  7  8  7  8  5  9  6
## [4369] NA  6  7  7  8  8  8  8  7  7  8  5  4 NA  7  8  6  9  8 NA  4 NA  9  7
## [4393]  7  7 NA  9  6  8  7  8  6  9  8 NA  5  5 10 NA  6  8  6  4  4  7  9  9
## [4417]  9  8 NA  9  4  8  5  6  8  8  6  8  8  7  7 10  7  7 NA  7  8  9  7  6
## [4441] 10  4 10  9  9  9 10 NA  6  6 NA  6  5  6  7  9 NA  8  5  4 NA  6 NA  6
## [4465]  6  6  5  4  4  7  9  7  7  5  6 NA  4  9  4  7  8  9  6 10  7  7  7 10
## [4489] NA  6  9  8  5  5  7  8  6  4  5  9  8  9  9  6  6  7  8  9 10 NA  8 10
## [4513]  7  9  8 NA  7  5  8  8  6  7  6  6  6  5  6  8  9 10  6  9  8  7  8 NA
## [4537] NA  6  6  6  6  7  7  6 10  6  7  4  7  5  6  4  6 NA  7  6  7  6  7  7
## [4561]  7 NA  8  8  7  7  7  7  7  6  4  7  8  5 NA  8 NA  7  9  9  6  8  6 10
## [4585]  7  5  8  9  9  7  8  6  8  8  5  7  7  7  7  9 NA  4 10  4  8  5  9  7
## [4609]  8  4  8  8  8  8  7  7  6  6 NA  6  4  6  7  8  4  4  7  9  4  8  9 NA
## [4633]  8  7 10  6  7  6  7  7  9  9  8  9  6  6  8  7 10  4  8  6  6  5  9 NA
## [4657]  6  6  5  5  6  9 10  6  6  5  8  8  7  6  9  8  8 NA  7  6  8  8  8  5
## [4681]  8  7  6  8  7  8  7  7  9  5  6  6  7  6  6  7  9 NA  8 NA  6  4  8  8
## [4705]  7  6  6  8  8  8  8  8  8  6  5  7  8  5  7  9 NA  9  7 NA  6  7  5  5
## [4729] NA  7 10  7  7  9  6  4  6  6  4  7  6  5  8  7  7  8  7 NA  6  5  7  6
## [4753]  8  7  8  6  5 10  7  8 NA  7  9  5 10  7  6  6  7  8  7  8  8  7  6  7
## [4777] 10  7  9  6  7 NA NA  5  9 10  6  6  7  6  5  9  6  7  5  8  7  4  9  8
## [4801]  7  7 10  8  7  5  7  8  7  6  6  8  6  4 NA  7  8  8  5  7  6  6  6  7
## [4825] 10  6  7  7  7 NA  7  6  9  5  8  6  4  6  6  5  8  5  6  7  6  6  6  6
## [4849]  8  6  7  9  8  5  8  9  6  5  6  7  8  6  4  5  8 10  7  9  5  6  4  6
## [4873]  8  6 10 10  4  6  8  5  9  9  5  7  7  8  7  8  5  9  9  7 NA NA  7 NA
## [4897]  7  7  5  5 10  7  7  9  8  8  5  7  6  6  7  8  7  9  9  9  7  6  7  9
## [4921]  9  4  7  4  7  6  6  8  6  7  6  7  6  8  7  7  6  8  8  7  7  8  8  7
## [4945]  9  8 10  8  9  9  7  5  9  6  7 10  5  6  6  7  8  8 NA  6  5  6  8  7
## [4969]  4  4  7  8  6  8  5  7  7  8  5  5 NA  5 NA  9 NA  8  8  8  7 10  7  8
## [4993]  6  6  9  6  8  8  7  4  9  6  7  5  6  6  7  6 10  7  8  8  6  6  6  8
## [5017]  8  7  7 10  7  4  8  8  9  8  6 NA  7  9  9 NA  8  9  7 10  9  6  7  8
## [5041] 10  8  7  9  7  6  8  6 10 NA  8  9  7  7  7  5  7  8  5  9  7  7  5  6
## [5065]  5  6  7  8  4  7  7  6  6  9 10  4  6  7  8  7  7  8  8  8  7  7  8  7
## [5089]  8  6  8  9  5  5  8  7 NA  8  6  8  8  6  9  7  5  5  8  5  5  8  5  8
## [5113]  8  4  8  5  6  9  6  7  6  6  5  7  7  8  7 NA  8  6  5  8  6  7  6  6
## [5137]  4  8  4  9  9  6 NA 10  7  7  9  5  7  8  8  7  7  7  8  7  7  6 10  6
## [5161]  8 10  5  8 10  6  6  7  6 10  7  6  6  8  8 NA  5  7  7  6  9  8  7  6
## [5185] 10  5  6  7  8  5  6  8 NA  6  7  6  7  7  9  8  7  7 10  6  7  6  8 10
## [5209]  7  7  7  5  7 10  8  9  9  6 10  4  7  4  4  8  9  4  7  9 10 NA  5  5
## [5233]  7 10  6 NA  5  7 NA  7  8  8  7  7  7  7  6  5  7  6 NA  7  8  5 10  4
## [5257]  9  7  6  5  7  7  9  7  7  8  7  7  7  8  6  6  8  5  7  6  8  9  6  8
## [5281]  7  6  7  9  7  9  7  5  7  7  6 10  9  7  9 NA  5  8  8  6  6  8  4  8
## [5305]  7 NA  8  6  5  9  7  7  8  6  8  8  9  9  7  8 NA  7  7  4  9  8  7  7
## [5329]  6  6  8  5  5  8  7  7  7 10  7  7 10  7 10 NA  5 10  6  8 10  9  6  8
## [5353]  8  6  8  6  7  5 NA  7  5  8  8  8  9  8  7  7 10  8  7  7 NA  5 10  8
## [5377]  5  7  9  6  6 NA  8  6  8 NA  6  7  8  6  8  9  6 10  9  7 NA  6 NA  7
## [5401]  5  4  7  7  6  5  4  6  8  7  8  8  8  5  6 10  4  7  8  4  6 10  7  6
## [5425] NA  6 10  6  6  5  7  7  9 NA  8  7  4  6  6 10  8  7  4  4  8  8  6  7
## [5449]  7  7  6  8  9  6  5  7  8  8  8  8  7  7  8  7  7  7  9  7  6  6  8  6
## [5473]  7 NA  5  5  6  5  8 10  6  6  6  8  8  7  5  6  7  7  7  8  5  7  7  6
## [5497]  6  8  5 10  8  7  7  8  6  6  9  6  7  6  7  8 10  6  5  7  6 NA  8 10
## [5521]  4  7  8  7  7  8  7  8  4  6  6  7  6  8  7  5 NA  8  7 NA  8  6  9  9
## [5545]  4  7  6  7  6  6  8  5  7  5  9  7  8  7  7  7  9  6  4  6  5  8  7  8
## [5569]  7 NA NA  9  7  9  7  7  6  9  6  7  5 NA  9  8 10  7  9  8  7  8  6  4
## [5593]  6  4  4  8  8  8  8  4  9  8  8 10  8  5  8  5  7  7  5  5  7  9  8  8
## [5617]  5  7 10  7  9  9  8  7  6  7  6  7  5 NA  6  6  6  7  4  6  7  8 NA  6
## [5641]  7  8  9 NA  6  6  9  6  5  7  9  6  6  6  8  7  9  5  6  6  7  8  6  6
## [5665]  8  8  4  7  7  6  6  6  4  6  5  7  5  8  5  9  8  5  7  6  8 10  6  7
## [5689]  9  8  9  8  7  7  5  6  6  6  7  7 NA  8  9 NA NA  8  8  8  9  8  9  7
## [5713]  6  9 10  9  7  9  8  5  7  7  9  7  6  8  4  6  8  7  8  7  7  6  8  5
## [5737]  7  9  6  5  4 NA  8  6  5  7  5  9  4  5  7  8  9  8  9  7  6  9  9  8
## [5761] NA  9  8  7  8  8  8  7  6  9  6  7 NA  9  7  9 10  7  8  8  7  8  8 NA
## [5785] 10  7  9  9  4  9  9  7  8  8  9  6  9  5  4  8  9  7  4  5  8  7  9  7
## [5809]  6  7  9  9  7  7  8  6  8  7  7  7 10  6  6  9  8  5  7  8  6  8  7  6
## [5833]  9  9  7  8  9  6  8  6  5  6  5  8  6  5  8  8  7  6  6  9  6  6  8  8
## [5857]  7  9  6  8  9  6  6  7  7  8  7  7  6  7  9  9  4  6  7  7  7  6  6  6
## [5881]  8  8  6  9  8  6  7  8  5  5  8  6  9 10  8  8  5  5  7  5  7  6  7  7
## [5905]  7  6  5  7  4  9  8  6  8  6  7  6  7  5  7  5 10 NA  7  8  5  6  8  7
## [5929]  6  8  7  8  8  6  7  6  8  8  6 NA  9  7  8  7  7  7  6  7  4  6  8  8
## [5953] NA  8  8  7  6  8  7  6  6  7  9  7  7  8  8  7 NA  6  9  6  9  7  7  8
## [5977]  6  8  7  8  6  6  4  6  6  6  7  8  8  8 NA  7  7  8  8  5  7  4  4  6
## [6001]  7  6  4  8  6  8  6  6  8  6  7  7  8  6  8  5  8  8  7 NA  7  8  6  7
## [6025]  8  8 10  7 NA  6  5 NA  6  7  8  6  6  9
czynniki5 <- hotdeck(czynniki4)
miss_var_summary(czynniki5)
## # A tibble: 40 × 3
##    variable                   n_miss pct_miss
##    <chr>                       <int>    <num>
##  1 Hours_Studied                   0        0
##  2 Attendance                      0        0
##  3 Parental_Involvement            0        0
##  4 Access_to_Resources             0        0
##  5 Extracurricular_Activities      0        0
##  6 Sleep_Hours                     0        0
##  7 Previous_Scores                 0        0
##  8 Motivation_Level                0        0
##  9 Internet_Access                 0        0
## 10 Tutoring_Sessions               0        0
## # ℹ 30 more rows

Reguły walidacyjne

rules <- validator(
Hours_Studied >= 0,
Hours_Studied <= 168,
Attendance >= 0, 
Attendance <= 100,
Sleep_Hours >= 0,
Sleep_Hours <= 24, 
Previous_Scores >= 0, 
Previous_Scores <= 100, 
Physical_Activity >= 0,
Physical_Activity <= 168,
Exam_Score >= 0,
Exam_Score <= 100,
Sleep_Hours * 7 + Hours_Studied + Physical_Activity >= 0,
Sleep_Hours * 7 + Hours_Studied + Physical_Activity <= 168
)

wyniki <- confront(czynniki5, rules)
summary(wyniki)
##    name items passes fails nNA error warning
## 1   V01  6038   6038     0   0 FALSE   FALSE
## 2   V02  6038   6038     0   0 FALSE   FALSE
## 3   V03  6038   6038     0   0 FALSE   FALSE
## 4   V04  6038   6038     0   0 FALSE   FALSE
## 5   V05  6038   6038     0   0 FALSE   FALSE
## 6   V06  6038   6038     0   0 FALSE   FALSE
## 7   V07  6038   6038     0   0 FALSE   FALSE
## 8   V08  6038   6038     0   0 FALSE   FALSE
## 9   V09  6038   6038     0   0 FALSE   FALSE
## 10  V10  6038   6038     0   0 FALSE   FALSE
## 11  V11  6038   6038     0   0 FALSE   FALSE
## 12  V12  6038   6037     1   0 FALSE   FALSE
## 13  V13  6038   6038     0   0 FALSE   FALSE
## 14  V14  6038   6038     0   0 FALSE   FALSE
##                                                            expression
## 1                                         Hours_Studied - 0 >= -1e-08
## 2                                        Hours_Studied - 168 <= 1e-08
## 3                                            Attendance - 0 >= -1e-08
## 4                                           Attendance - 100 <= 1e-08
## 5                                           Sleep_Hours - 0 >= -1e-08
## 6                                           Sleep_Hours - 24 <= 1e-08
## 7                                       Previous_Scores - 0 >= -1e-08
## 8                                      Previous_Scores - 100 <= 1e-08
## 9                                     Physical_Activity - 0 >= -1e-08
## 10                                   Physical_Activity - 168 <= 1e-08
## 11                                           Exam_Score - 0 >= -1e-08
## 12                                          Exam_Score - 100 <= 1e-08
## 13  Sleep_Hours * 7 + Hours_Studied + Physical_Activity - 0 >= -1e-08
## 14 Sleep_Hours * 7 + Hours_Studied + Physical_Activity - 168 <= 1e-08
plot(wyniki)

dane_zwalidowane <- czynniki5 %>%
  replace_errors(rules)
errors_removed(dane_zwalidowane)
## call:  locate_errors(data, x, ref, ..., cl = cl, Ncpus = Ncpus) 
## located  1  error(s).
## located  0  missing value(s).
## Use 'summary', 'values', '$errors' or '$weight', to explore and retrieve the errors.
par(mfrow=c(2,3))
boxplot(dane_zwalidowane$Hours_Studied, main="Hours Studied") 
boxplot(dane_zwalidowane$Attendance, main="Attendance")
boxplot(dane_zwalidowane$Sleep_Hours, main="Sllep Hours")
boxplot(dane_zwalidowane$Previous_Scores, main="Previos Scores")
boxplot(dane_zwalidowane$Tutoring_Sessions, main="Tutoring Sessions")
boxplot(dane_zwalidowane$Exam_Score, main="Exam Score")

par(mfrow=c(2,3)) #zmienić przy kolejnych wykresach na c(1,1) bo będzie pamiętać i tworzyć wykresy w blokach 6- wykresowych
boxplot(dane_zwalidowane$Hours_Studied, main="Hours Studied") 
boxplot(dane_zwalidowane$Attendance, main="Attendance")
boxplot(dane_zwalidowane$Sleep_Hours, main="Sllep Hours")
boxplot(dane_zwalidowane$Previous_Scores, main="Previos Scores")
boxplot(dane_zwalidowane$Tutoring_Sessions, main="Tutoring Sessions")
boxplot(dane_zwalidowane$Exam_Score, main="Exam Score")
ggplot(dane_zwalidowane, aes(x=Attendance)) +
  geom_boxplot() +
  theme_bw() +
  coord_flip()

ggplot(dane_zwalidowane, aes(x=Hours_Studied)) +
  geom_boxplot() +
  theme_bw() +
  coord_flip()

ggplot(dane_zwalidowane, aes(x=Sleep_Hours)) +
  geom_boxplot() +
  theme_bw() +
  coord_flip()

ggplot(dane_zwalidowane, aes(x=Previous_Scores)) +
  geom_boxplot() +
  theme_bw() +
  coord_flip()

ggplot(dane_zwalidowane, aes(x=Tutoring_Sessions)) +
  geom_boxplot() +
  theme_bw() +
  coord_flip()

ggplot(dane_zwalidowane, aes(x=Exam_Score)) +
  geom_boxplot() +
  theme_bw() +
  coord_flip()

grubbs.test(dane_zwalidowane$Hours_Studied)
## 
##  Grubbs test for one outlier
## 
## data:  dane_zwalidowane$Hours_Studied
## G = 4.01539, U = 0.99733, p-value = 0.1773
## alternative hypothesis: highest value 44 is an outlier
grubbs.test(dane_zwalidowane$Attendance)
## 
##  Grubbs test for one outlier
## 
## data:  dane_zwalidowane$Attendance
## G = 1.72722, U = 0.99951, p-value = 1
## alternative hypothesis: lowest value 60 is an outlier
grubbs.test(dane_zwalidowane$Sleep_Hours)
## 
##  Grubbs test for one outlier
## 
## data:  dane_zwalidowane$Sleep_Hours
## G = 2.0532, U = 0.9993, p-value = 1
## alternative hypothesis: lowest value 4 is an outlier
grubbs.test(dane_zwalidowane$Previous_Scores)
## 
##  Grubbs test for one outlier
## 
## data:  dane_zwalidowane$Previous_Scores
## G = 1.7435, U = 0.9995, p-value = 1
## alternative hypothesis: lowest value 50 is an outlier
grubbs.test(dane_zwalidowane$Tutoring_Sessions)
## 
##  Grubbs test for one outlier
## 
## data:  dane_zwalidowane$Tutoring_Sessions
## G = 5.25143, U = 0.99543, p-value = 0.0004415
## alternative hypothesis: highest value 8 is an outlier
grubbs.test(dane_zwalidowane$Exam_Score)
## 
##  Grubbs test for one outlier
## 
## data:  dane_zwalidowane$Exam_Score
## G = 8.38735, U = 0.98834, p-value < 2.2e-16
## alternative hypothesis: highest value 100 is an outlier
ggplot(dane_zwalidowane, aes(x = Gender, fill = Gender))+
  geom_bar()+
  scale_fill_manual(values =c("Female"="pink","Male"="lightblue"))+
  theme_minimal()+
  ggtitle("Podział płci w próbie")+
  theme(plot.title = element_text(hjust =0.5))

ggplot(dane_zwalidowane, aes(x = Exam_Score, fill = Exam_Score))+
  geom_histogram(binwidth =5,fill="#5C1C81", color ="black")+
  theme_minimal()+
  ggtitle("Rozkład wyników egzaminów")+
  theme(plot.title = element_text(hjust =0.5))

 w1 <- ggplot(dane_zwalidowane, aes(x = Exam_Score))+
  geom_histogram(binwidth =5, fill ="steelblue", color ="black")+
  theme_minimal()+
  labs(title ="Rozkład wyników egzaminów", x ="Wynik egzaminu", y ="Liczba uczniów")+
  facet_grid(~Gender)
w2 <-ggplot(dane_zwalidowane, aes(x = Hours_Studied))+
  geom_histogram(binwidth =5, fill ="darkgreen", color ="black")+
  theme_minimal()+
  labs(title ="Rozkład godzin nauki", x ="Godziny nauki w tygodniu", y="Liczba uczniów")+
  facet_grid(~Gender)
grid.arrange(w1, w2, nrow = 1)

ggplot(dane_zwalidowane, aes(x = Hours_Studied, y = Exam_Score))+
  geom_point(color ="blue", alpha =0.6)+
  geom_smooth(method ="lm", color ="red", se =FALSE)+
  theme_minimal()+
  labs(title ="Relacja między godzinami nauki a wynikiem egzaminu",
       x ="Godziny nauki w tygodniu",
       y ="Wynik egzaminu")
## `geom_smooth()` using formula = 'y ~ x'

ggplot(dane_zwalidowane, aes(x = Parental_Involvement, y = Exam_Score, fill = Parental_Involvement))+
  geom_violin()+
  theme_minimal()+
  labs(title ="Wyniki egzaminów w zależności od zaangażowania rodziców",
       x ="Zaangażowanie rodziców",
       y ="Wynik egzaminu")+
  scale_fill_brewer(palette ="Set2")

# Wykres słupkowy typów szkół
ggplot(dane_zwalidowane, aes(x = School_Type, fill = School_Type))+
  geom_bar()+
  theme_minimal()+
  labs(title ="Rozkład typów szkół",
       x ="Typ szkoły",
       y ="Liczba uczniów")+
  scale_fill_brewer(palette ="Set1")

ggplot(dane_zwalidowane, aes(x = School_Type, y = Exam_Score, fill = School_Type))+
  geom_boxplot()+
  theme_minimal()+
  labs(title ="Wyniki egzaminów w zależności od typów szkół",
       x ="Typ Szkoły",
       y ="Wynik egzaminu")+
  scale_fill_brewer(palette ="Set2")

ggplot(dane_zwalidowane, aes(x = Parental_Involvement, y = Exam_Score, fill = Parental_Involvement))+
  geom_boxplot()+
  facet_wrap(~ Motivation_Level)+
  theme_minimal()+
  labs(title ="Wyniki egzaminów w zależności od motywacji i zaangażowania rodziców",
       x ="Zaangażowanie rodziców",
       y ="Wynik egzaminu")+
  scale_fill_brewer(palette ="Set3")

ggplot(dane_zwalidowane, aes(x = Access_to_Resources, y = Exam_Score, fill = Access_to_Resources))+
  geom_boxplot()+
  facet_wrap(~ Internet_Access)+
  theme_minimal()+
  labs(title ="Wyniki egzaminów w zależności od dostępu do źródeł i internetu",
       x ="Dostęp do źródeł",
       y ="Wynik egzaminu")+
  scale_fill_brewer(palette ="Set5")

ggplot(dane_zwalidowane, aes(x = Exam_Score))+
  geom_histogram(binwidth =5, fill ="steelblue", color ="black")+
  theme_minimal()+
  labs(title ="Rozkład wyników egzaminów", x ="Wynik egzaminu", y ="Liczba uczniów")+
  facet_grid(~Learning_Disabilities)

# Wykres heksagonalny
ggplot(dane_zwalidowane, aes(x = Distance_from_Home, y = Exam_Score)) +
  geom_hex(bins = 30) + # Liczba przedziałów (możesz dostosować np. 20, 40)
  scale_fill_viridis_c() + # Kolorystyka dla lepszej wizualizacji
  theme_minimal() +
  labs(
    title = "Zależność między wynikiem egzaminu a dystansem od domu",
    x = "Dystans od domu do szkoły",
    y = "Wynik Egzaminu",
    fill = "Gęstość"
  )

ld_counts <- dane_zwalidowane %>%
  count(Learning_Disabilities)%>%
  mutate(Percentage =round(n /sum(n)*100,1))# Zaokrąglamy do 1 miejsca po przecinku# Tworzenie wykresu kołowego
ggplot(ld_counts, aes(x ="", y = n, fill = Learning_Disabilities))+
  geom_bar(stat ="identity", width =1)+
  coord_polar("y", start =0)+
  scale_fill_manual(values =c("Yes"="red","No"="lightblue"))+
  theme_void()+
  ggtitle("Udział osób z trudnościami w uczeniu się")+
  theme(plot.title = element_text(hjust =0.5))+
  geom_text(aes(label = paste0(Percentage,"%")), 
            position = position_stack(vjust =0.5), 
            color ="black", size =5)

ggplot(dane_zwalidowane, aes(x = Exam_Score))+
  geom_histogram(binwidth =5, fill ="darkred", color ="black")+
  theme_minimal()+
  labs(title ="Rozkład wyników egzaminów", x ="Wynik egzaminu", y ="Poziom wykształcenia rodziców")+
  facet_grid(~Parental_Education_Level)

# Upewniamy się, że kategorie są w poprawnej kolejności
dane_zwalidowane$Teacher_Quality <- factor(dane_zwalidowane$Teacher_Quality, levels =c("Low","Medium","High"))# Obliczenie mediany wyników egzaminów dla każdej kategorii jakości nauczycieli
median_scores <- dane_zwalidowane %>%
  group_by(Teacher_Quality)%>%
  summarise(Median_Exam_Score = median(Exam_Score, na.rm =TRUE))# Wykres liniowy z medianą
ggplot(median_scores, aes(x = Teacher_Quality, y = Median_Exam_Score, group =1))+
  geom_line(color ="#ff6347", size =1)+# Linia wykresu
  geom_point(color ="darkred", size =3)+# Punkty oznaczające medianę
  geom_text(aes(label =round(Median_Exam_Score,1)), vjust =-1)+# Etykiety mediany
  ylim(0,100)+# Skala od 0 do 100
  theme_minimal()+
  ggtitle("Mediana wyniku egzaminu a jakość nauczycieli")+
  xlab("Jakość nauczycieli")+
  ylab("Mediana wyniku egzaminu")+
  theme(plot.title = element_text(hjust =0.5))

ggplot(dane_zwalidowane, aes(x = Family_Income, y = Tutoring_Sessions, color = Family_Income)) +
  geom_jitter(width = 0.2, alpha = 0.7) + # Dodanie punktów z małym zakłóceniem na osi X (w celu uniknięcia nakładania punktów)
  geom_smooth(method = "lm", se = FALSE, color = "black") + # Linia trendu (regresji liniowej)
  scale_color_manual(values = c("High" = "lightgreen", "Medium" = "lightblue", "Low" = "lightpink")) +
  theme_minimal() +
  labs(
    title = "Wpływ dochodów rodziny na liczbę korepetycji",
    x = "Dochód rodziny",
    y = "Liczba korepetycji",
    color = "Dochód"
  )
## `geom_smooth()` using formula = 'y ~ x'

ld_counts <- dane_zwalidowane %>%
  count(Family_Income)%>%
  mutate(Percentage =round(n /sum(n)*100,1))# Zaokrąglamy do 1 miejsca po przecinku# Tworzenie wykresu kołowego
ggplot(ld_counts, aes(x ="", y = n, fill = Family_Income))+
  geom_bar(stat ="identity", width =1)+
  coord_polar("y", start =0)+
  scale_fill_manual(values =c("Low"="lightpink","Medium"="lightblue","High"="lightgreen"))+
  theme_void()+
  ggtitle("Poziom dochodów rodziców")+
  theme(plot.title = element_text(hjust =0.5))+
  geom_text(aes(label = paste0(Percentage,"%")), 
            position = position_stack(vjust =0.5), 
            color ="black", size =5)

ggplot(dane_zwalidowane, aes(x = Sleep_Hours, y = Exam_Score)) +
  geom_jitter(color = "purple", alpha = 0.5) +
  geom_smooth(method = "lm", color = "orange", se = TRUE) +
  theme_minimal() +
  labs(title = "Relacja między godzinami snu a wynikiem egzaminu",
       x = "Godziny snu",
       y = "Wynik egzaminu")
## `geom_smooth()` using formula = 'y ~ x'

zmienne_ilosciowe <- dane_zwalidowane %>%
  select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores, 
         Tutoring_Sessions, Physical_Activity, Exam_Score)

data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Hours_Studied
stat_desc <- data %>%
  summarise(
    średnia = mean(Hours_Studied, na.rm = TRUE),
    mediana = median(Hours_Studied, na.rm = TRUE),
    odchylenie_standardowe = sd(Hours_Studied, na.rm = TRUE),
    minimum = min(Hours_Studied, na.rm = TRUE),
    maksimum = max(Hours_Studied, na.rm = TRUE)
  ) %>%
  pivot_longer(
    cols = everything(),  # Wszystkie kolumny przekształcamy w długą tabelę
    names_to = "Statystyka",
    values_to = "Wartość"
  ) 

stat_desc %>%
  gt() %>%
  tab_header(
    title = "Statystyki Opisowe:",
    subtitle = "Hours_Studied"
  ) %>%
  fmt_number(
    columns = Wartość,
    decimals = 2
  ) %>%
  data_color(
    columns = Wartość,
    colors = scales::col_numeric(
      palette = c("purple", "pink", "lightblue"),
      domain = NULL
    )
  ) %>%
  cols_label(
    Statystyka = "Rodzaj statystyki",
    Wartość = "Wartość"
  ) %>%
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels()
  )
Statystyki Opisowe:
Hours_Studied
Rodzaj statystyki Wartość
średnia 19.99
mediana 20.00
odchylenie_standardowe 5.98
minimum 1.00
maksimum 44.00
 
zmienne_ilosciowe <- dane_zwalidowane %>%
  select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores, 
         Tutoring_Sessions, Physical_Activity, Exam_Score)

data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Attendance
stat_desc <- data %>%
  summarise(
    średnia = mean(Attendance, na.rm = TRUE),
    mediana = median(Attendance, na.rm = TRUE),
    odchylenie_standardowe = sd(Attendance, na.rm = TRUE),
    minimum = min(Attendance, na.rm = TRUE),
    maksimum = max(Attendance, na.rm = TRUE)
  ) %>%
  pivot_longer(
    cols = everything(),  # Wszystkie kolumny przekształcamy w długą tabelę
    names_to = "Statystyka",
    values_to = "Wartość"
  ) 


stat_desc %>%
  gt() %>%
  tab_header(
    title = "Statystyki Opisowe:",
    subtitle = "Attendance"
  ) %>%
  fmt_number(
    columns = Wartość,
    decimals = 2
  ) %>%
  data_color(
    columns = Wartość,
    colors = scales::col_numeric(
      palette = c("purple", "pink", "lightblue"),
      domain = NULL
    )
  ) %>%
  cols_label(
    Statystyka = "Rodzaj statystyki",
    Wartość = "Wartość"
  ) %>%
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels()
  )
Statystyki Opisowe:
Attendance
Rodzaj statystyki Wartość
średnia 80.02
mediana 80.00
odchylenie_standardowe 11.59
minimum 60.00
maksimum 100.00
 
zmienne_ilosciowe <- dane_zwalidowane %>%
  select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores, 
         Tutoring_Sessions, Physical_Activity, Exam_Score)

data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Sleep_Hours
stat_desc <- data %>%
  summarise(
    średnia = mean(Sleep_Hours, na.rm = TRUE),
    mediana = median(Sleep_Hours, na.rm = TRUE),
    odchylenie_standardowe = sd(Sleep_Hours, na.rm = TRUE),
    minimum = min(Sleep_Hours, na.rm = TRUE),
    maksimum = max(Sleep_Hours, na.rm = TRUE)
  ) %>%
  pivot_longer(
    cols = everything(),  # Wszystkie kolumny przekształcamy w długą tabelę
    names_to = "Statystyka",
    values_to = "Wartość"
  ) 

stat_desc %>%
  gt() %>%
  tab_header(
    title = "Statystyki Opisowe:",
    subtitle = "Sleep_Hours"
  ) %>%
  fmt_number(
    columns = Wartość,
    decimals = 2
  ) %>%
  data_color(
    columns = Wartość,
    colors = scales::col_numeric(
      palette = c("purple", "pink", "lightblue"),
      domain = NULL
    )
  ) %>%
  cols_label(
    Statystyka = "Rodzaj statystyki",
    Wartość = "Wartość"
  ) %>%
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels()
  )
Statystyki Opisowe:
Sleep_Hours
Rodzaj statystyki Wartość
średnia 7.03
mediana 7.00
odchylenie_standardowe 1.48
minimum 4.00
maksimum 10.00
 
zmienne_ilosciowe <- dane_zwalidowane %>%
  select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores, 
         Tutoring_Sessions, Physical_Activity, Exam_Score)

data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Tutoring_Sessions
stat_desc <- data %>%
  summarise(
    średnia = mean(Tutoring_Sessions, na.rm = TRUE),
    mediana = median(Tutoring_Sessions, na.rm = TRUE),
    odchylenie_standardowe = sd(Tutoring_Sessions, na.rm = TRUE),
    minimum = min(Tutoring_Sessions, na.rm = TRUE),
    maksimum = max(Tutoring_Sessions, na.rm = TRUE)
  ) %>%
  pivot_longer(
    cols = everything(),  # Wszystkie kolumny przekształcamy w długą tabelę
    names_to = "Statystyka",
    values_to = "Wartość"
  ) 

stat_desc %>%
  gt() %>%
  tab_header(
    title = "Statystyki Opisowe:",
    subtitle = "Tutoring_Sessions"
  ) %>%
  fmt_number(
    columns = Wartość,
    decimals = 2
  ) %>%
  data_color(
    columns = Wartość,
    colors = scales::col_numeric(
      palette = c("purple", "pink", "lightblue"),
      domain = NULL
    )
  ) %>%
  cols_label(
    Statystyka = "Rodzaj statystyki",
    Wartość = "Wartość"
  ) %>%
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels()
  )
Statystyki Opisowe:
Tutoring_Sessions
Rodzaj statystyki Wartość
średnia 1.50
mediana 1.00
odchylenie_standardowe 1.24
minimum 0.00
maksimum 8.00
 
zmienne_ilosciowe <- dane_zwalidowane %>%
  select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores, 
         Tutoring_Sessions, Physical_Activity, Exam_Score)

data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Physical_Activity
stat_desc <- data %>%
  summarise(
    średnia = mean(Physical_Activity, na.rm = TRUE),
    mediana = median(Physical_Activity, na.rm = TRUE),
    odchylenie_standardowe = sd(Physical_Activity, na.rm = TRUE),
    minimum = min(Physical_Activity, na.rm = TRUE),
    maksimum = max(Physical_Activity, na.rm = TRUE)
  ) %>%
  pivot_longer(
    cols = everything(),  # Wszystkie kolumny przekształcamy w długą tabelę
    names_to = "Statystyka",
    values_to = "Wartość"
  ) 


stat_desc %>%
  gt() %>%
  tab_header(
    title = "Statystyki Opisowe:",
    subtitle = "Physical_Activity"
  ) %>%
  fmt_number(
    columns = Wartość,
    decimals = 2
  ) %>%
  data_color(
    columns = Wartość,
    colors = scales::col_numeric(
      palette = c("purple", "pink", "lightblue"),
      domain = NULL
    )
  ) %>%
  cols_label(
    Statystyka = "Rodzaj statystyki",
    Wartość = "Wartość"
  ) %>%
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels()
  )
Statystyki Opisowe:
Physical_Activity
Rodzaj statystyki Wartość
średnia 2.97
mediana 3.00
odchylenie_standardowe 1.03
minimum 0.00
maksimum 6.00
 
zmienne_ilosciowe <- dane_zwalidowane %>%
  select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores, 
         Tutoring_Sessions, Physical_Activity, Exam_Score)

data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Exam_Score
stat_desc <- data %>%
  summarise(
    średnia = mean(Exam_Score, na.rm = TRUE),
    mediana = median(Exam_Score, na.rm = TRUE),
    odchylenie_standardowe = sd(Exam_Score, na.rm = TRUE),
    minimum = min(Exam_Score, na.rm = TRUE),
    maksimum = max(Exam_Score, na.rm = TRUE)
  ) %>%
  pivot_longer(
    cols = everything(),  # Wszystkie kolumny przekształcamy w długą tabelę
    names_to = "Statystyka",
    values_to = "Wartość"
  ) 


stat_desc %>%
  gt() %>%
  tab_header(
    title = "Statystyki Opisowe:",
    subtitle = "Exam_Score"
  ) %>%
  fmt_number(
    columns = Wartość,
    decimals = 2
  ) %>%
  data_color(
    columns = Wartość,
    colors = scales::col_numeric(
      palette = c("purple", "pink", "lightblue"),
      domain = NULL
    )
  ) %>%
  cols_label(
    Statystyka = "Rodzaj statystyki",
    Wartość = "Wartość"
  ) %>%
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels()
  )
Statystyki Opisowe:
Exam_Score
Rodzaj statystyki Wartość
średnia 67.26
mediana 67.00
odchylenie_standardowe 3.90
minimum 56.00
maksimum 100.00
 
# Statystyki opisowe dla zmiennych ilościowych
zmienne_ilosciowe <- dane_zwalidowane %>%
  select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores, 
         Tutoring_Sessions, Physical_Activity, Exam_Score)


 
#. Macierz korelacji dla zmiennych ilościowych
macierz_korelacji <- cor(zmienne_ilosciowe, use = "complete.obs")
print(macierz_korelacji)
##                   Hours_Studied   Attendance   Sleep_Hours Previous_Scores
## Hours_Studied       1.000000000 -0.001527627  0.0126840091     0.017698977
## Attendance         -0.001527627  1.000000000 -0.0185058862    -0.016306714
## Sleep_Hours         0.012684009 -0.018505886  1.0000000000    -0.015346396
## Previous_Scores     0.017698977 -0.016306714 -0.0153463956     1.000000000
## Tutoring_Sessions  -0.013941975  0.014743286 -0.0091340906    -0.020365357
## Physical_Activity   0.005044221 -0.018809595 -0.0009687035    -0.005460835
## Exam_Score          0.413230008  0.550146082 -0.0099490753     0.161328016
##                   Tutoring_Sessions Physical_Activity   Exam_Score
## Hours_Studied          -0.013941975      0.0050442207  0.413230008
## Attendance              0.014743286     -0.0188095947  0.550146082
## Sleep_Hours            -0.009134091     -0.0009687035 -0.009949075
## Previous_Scores        -0.020365357     -0.0054608345  0.161328016
## Tutoring_Sessions       1.000000000      0.0151666001  0.136875188
## Physical_Activity       0.015166600      1.0000000000  0.036946720
## Exam_Score              0.136875188      0.0369467196  1.000000000
# Wizualizacja macierzy korelacji
corrplot(macierz_korelacji, method = "circle", type = "upper", 
         tl.col = "black", tl.srt = 45, col = colorRampPalette(c("blue", "white", "red"))(200))

 dane_zwalidowane %>%
   filter(Learning_Disabilities %in% c("Yes", "No")) %>%
   ggbetweenstats(
     y=Exam_Score,
     x=Learning_Disabilities
   )

 dane_zwalidowane %>%
   filter(Extracurricular_Activities %in% c("Yes", "No")) %>%
   ggbetweenstats(
     y=Exam_Score,
     x=Extracurricular_Activities
   )

set.seed(123)
  gghistostats(
  data       = dane_zwalidowane,
  x          = Attendance,
  title      = "Wpływ frekwencji na wynik egzaminu",
  test.value = 12,
  binwidth   = 1
)